Convex hull (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Convex hull" in English language version.

Last modified: 15:05:55, 12 August 2026 (UTC)

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McCallum & Avis (1979); Graham & Yao (1983); Lee (1983). McCallum, Duncan; Avis, David (1979), "A linear algorithm for finding the convex hull of a simple polygon", Information Processing Letters, 9 (5): 201–206, doi:10.1016/0020-0190(79)90069-3, MR 0552534 Graham, Ronald L.; Yao, F. Frances (1983), "Finding the convex hull of a simple polygon", Journal of Algorithms, 4 (4): 324–331, Bibcode:1983JAlgo...4..324G, doi:10.1016/0196-6774(83)90013-5, MR 0729228 Lee, D. T. (1983), "On finding the convex hull of a simple polygon", International Journal of Computer and Information Sciences, 12 (2): 87–98, doi:10.1007/BF00993195, MR 0724699
Laurentini (1994). Laurentini, A. (1994), "The visual hull concept for silhouette-based image understanding", IEEE Transactions on Pattern Analysis and Machine Intelligence, 16 (2): 150–162, Bibcode:1994ITPAM..16..150L, doi:10.1109/34.273735
Edelsbrunner, Kirkpatrick & Seidel (1983). Edelsbrunner, Herbert; Kirkpatrick, David G.; Seidel, Raimund (1983), "On the shape of a set of points in the plane", IEEE Transactions on Information Theory, 29 (4): 551–559, Bibcode:1983ITIT...29..551E, doi:10.1109/TIT.1983.1056714
Chazelle (1985). Chazelle, Bernard (1985), "On the convex layers of a planar set", IEEE Transactions on Information Theory, 31 (4): 509–517, Bibcode:1985ITIT...31..509C, doi:10.1109/TIT.1985.1057060, MR 0798557
Kernohan, Gitzen & Millspaugh (2001), p. 137–140; Nilsen, Pedersen & Linnell (2008) Kernohan, Brian J.; Gitzen, Robert A.; Millspaugh, Joshua J. (2001), "Analysis of animal space use and movements", in Millspaugh, Joshua; Marzluff, John M. (eds.), Radio Tracking and Animal Populations, Academic Press, ISBN 9780080540221 Nilsen, Erlend B.; Pedersen, Simen; Linnell, John D. C. (2008), "Can minimum convex polygon home ranges be used to draw biologically meaningful conclusions?", Ecological Research, 23 (3): 635–639, Bibcode:2008EcoR...23..635N, doi:10.1007/s11284-007-0421-9
Worton (1995). Worton, Bruce J. (1995), "A convex hull-based estimator of home-range size", Biometrics, 51 (4): 1206–1215, Bibcode:1995Biome..51.1206W, doi:10.2307/2533254, JSTOR 2533254
Getz & Wilmers (2004). Getz, Wayne M.; Wilmers, Christopher C. (2004), "A local nearest-neighbor convex-hull construction of home ranges and utilization distributions" (PDF), Ecography, 27 (4), Wiley: 489–505, Bibcode:2004Ecogr..27..489G, doi:10.1111/j.0906-7590.2004.03835.x
Kirkpatrick (2006). Kirkpatrick, K. A. (2006), "The Schrödinger–HJW theorem", Foundations of Physics Letters, 19 (1): 95–102, arXiv:quant-ph/0305068, Bibcode:2006FoPhL..19...95K, doi:10.1007/s10702-006-1852-1
Kim et al. (2019). Kim, Sooran; Kim, Kyoo; Koo, Jahyun; Lee, Hoonkyung; Min, Byung Il; Kim, Duck Young (December 2019), "Pressure-induced phase transitions and superconductivity in magnesium carbides", Scientific Reports, 9 (1): 20253, Bibcode:2019NatSR...920253K, doi:10.1038/s41598-019-56497-6, PMC 6934831, PMID 31882982

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Rockafellar (1970), p. 12. Rockafellar, R. Tyrrell (1970), Convex Analysis, Princeton Mathematical Series, vol. 28, Princeton, N.J.: Princeton University Press, MR 0274683
Oberman (2007). Oberman, Adam M. (2007), "The convex envelope is the solution of a nonlinear obstacle problem", Proceedings of the American Mathematical Society, 135 (6): 1689–1694, doi:10.1090/S0002-9939-07-08887-9, MR 2286077
Knuth (1992). Knuth, Donald E. (1992), Axioms and Hulls, Lecture Notes in Computer Science, vol. 606, Heidelberg: Springer-Verlag, doi:10.1007/3-540-55611-7, ISBN 3-540-55611-7, MR 1226891, archived from the original on 2017-06-20, retrieved 2011-09-15
Rockafellar (1970), p. 12; Lay (1982), p. 17. Rockafellar, R. Tyrrell (1970), Convex Analysis, Princeton Mathematical Series, vol. 28, Princeton, N.J.: Princeton University Press, MR 0274683 Lay, Steven R. (1982), Convex Sets and their Applications, John Wiley & Sons, ISBN 0-471-09584-2, MR 0655598
Sontag (1982). Sontag, Eduardo D. (1982), "Remarks on piecewise-linear algebra", Pacific Journal of Mathematics, 98 (1): 183–201, doi:10.2140/pjm.1982.98.183, MR 0644949
Rockafellar (1970), p. 99. Rockafellar, R. Tyrrell (1970), Convex Analysis, Princeton Mathematical Series, vol. 28, Princeton, N.J.: Princeton University Press, MR 0274683
Steinitz (1914); Gustin (1947); Bárány, Katchalski & Pach (1982) Steinitz, E. (1914), "Bedingt konvergente Reihen und konvexe Systeme. (Fortsetzung)", Journal für die Reine und Angewandte Mathematik, 1914 (144): 1–40, doi:10.1515/crll.1914.144.1, MR 1580890 Gustin, William (1947), "On the interior of the convex hull of a Euclidean set", Bulletin of the American Mathematical Society, 53 (4): 299–301, doi:10.1090/S0002-9904-1947-08787-5, MR 0020800 Bárány, Imre; Katchalski, Meir; Pach, János (1982), "Quantitative Helly-type theorems", Proceedings of the American Mathematical Society, 86 (1): 109–114, doi:10.1090/S0002-9939-1982-0663877-X, JSTOR 2044407, MR 0663877
Grünbaum (2003), p. 16; Lay (1982), p. 21; Sakuma (1977). Grünbaum, Branko (2003), Convex Polytopes, Graduate Texts in Mathematics, vol. 221 (2nd ed.), Springer, ISBN 9780387004242 Lay, Steven R. (1982), Convex Sets and their Applications, John Wiley & Sons, ISBN 0-471-09584-2, MR 0655598 Sakuma, Itsuo (1977), "Closedness of convex hulls", Journal of Economic Theory, 14 (1): 223–227, doi:10.1016/0022-0531(77)90095-3
This example is given by Talman (1977), Remark 2.6. Talman, Louis A. (1977), "Fixed points for condensing multifunctions in metric spaces with convex structure", Kōdai Mathematical Seminar Reports, 29 (1–2): 62–70, MR 0463985
Whitley (1986). Whitley, Robert (1986), "The Kreĭn-Šmulian theorem", Proceedings of the American Mathematical Society, 97 (2): 376–377, doi:10.2307/2046536, JSTOR 2046536, MR 0835903
Krein & Milman (1940); Lay (1982), p. 43. Krein, Mark; Milman, David (1940), "On extreme points of regular convex sets", Studia Mathematica, 9: 133–138, doi:10.4064/sm-9-1-133-138 Lay, Steven R. (1982), Convex Sets and their Applications, John Wiley & Sons, ISBN 0-471-09584-2, MR 0655598
Okon (2000). Okon, T. (2000), "Choquet theory in metric spaces", Zeitschrift für Analysis und ihre Anwendungen, 19 (2): 303–314, doi:10.4171/ZAA/952, MR 1768994
Kiselman (2002). Kiselman, Christer O. (2002), "A semigroup of operators in convexity theory", Transactions of the American Mathematical Society, 354 (5): 2035–2053, doi:10.1090/S0002-9947-02-02915-X, MR 1881029
Kashiwabara, Nakamura & Okamoto (2005). Kashiwabara, Kenji; Nakamura, Masataka; Okamoto, Yoshio (2005), "The affine representation theorem for abstract convex geometries", Computational Geometry, 30 (2): 129–144, doi:10.1016/j.comgeo.2004.05.001, MR 2107032
Krein & Šmulian (1940), Theorem 3, pages 562–563; Schneider (1993), Theorem 1.1.2 (pages 2–3) and Chapter 3. Krein, M.; Šmulian, V. (1940), "On regularly convex sets in the space conjugate to a Banach space", Annals of Mathematics, Second Series, 41 (3): 556–583, doi:10.2307/1968735, hdl:10338.dmlcz/100106, JSTOR 1968735, MR 0002009 Schneider, Rolf (1993), Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge: Cambridge University Press, doi:10.1017/CBO9780511526282, ISBN 0-521-35220-7, MR 1216521
Demaine et al. (2008). Demaine, Erik D.; Gassend, Blaise; O'Rourke, Joseph; Toussaint, Godfried T. (2008), "All polygons flip finitely ... right?", Surveys on Discrete and Computational Geometry, Contemporary Mathematics, vol. 453, Providence, Rhode Island: American Mathematical Society, pp. 231–255, doi:10.1090/conm/453/08801, ISBN 978-0-8218-4239-3, MR 2405683
Cranston, Hsu & March (1989). Cranston, M.; Hsu, P.; March, P. (1989), "Smoothness of the convex hull of planar Brownian motion", Annals of Probability, 17 (1): 144–150, doi:10.1214/aop/1176991500, JSTOR 2244202, MR 0972777
Sedykh (1981). Sedykh, V. D. (1981), "Structure of the convex hull of a space curve", Trudy Seminara imeni I. G. Petrovskogo (6): 239–256, MR 0630708, translated in Journal of Soviet Mathematics 33 (4): 1140–1153, 1986, doi:10.1007/BF01086114
Dirnböck & Stachel (1997). Dirnböck, Hans; Stachel, Hellmuth (1997), "The development of the oloid" (PDF), Journal for Geometry and Graphics, 1 (2): 105–118, MR 1622664
Seaton (2017). Seaton, Katherine A. (2017), "Sphericons and D-forms: a crocheted connection", Journal of Mathematics and the Arts, 11 (4): 187–202, arXiv:1603.08409, doi:10.1080/17513472.2017.1318512, MR 3765242
Rockafellar (1970), p. 36. Rockafellar, R. Tyrrell (1970), Convex Analysis, Princeton Mathematical Series, vol. 28, Princeton, N.J.: Princeton University Press, MR 0274683
Rockafellar (1970), p. 149. Rockafellar, R. Tyrrell (1970), Convex Analysis, Princeton Mathematical Series, vol. 28, Princeton, N.J.: Princeton University Press, MR 0274683
Avis, Bremner & Seidel (1997). Avis, David; Bremner, David; Seidel, Raimund (1997), "How good are convex hull algorithms?", Computational Geometry, 7 (5–6): 265–301, doi:10.1016/S0925-7721(96)00023-5, MR 1447243
McCallum & Avis (1979); Graham & Yao (1983); Lee (1983). McCallum, Duncan; Avis, David (1979), "A linear algorithm for finding the convex hull of a simple polygon", Information Processing Letters, 9 (5): 201–206, doi:10.1016/0020-0190(79)90069-3, MR 0552534 Graham, Ronald L.; Yao, F. Frances (1983), "Finding the convex hull of a simple polygon", Journal of Algorithms, 4 (4): 324–331, Bibcode:1983JAlgo...4..324G, doi:10.1016/0196-6774(83)90013-5, MR 0729228 Lee, D. T. (1983), "On finding the convex hull of a simple polygon", International Journal of Computer and Information Sciences, 12 (2): 87–98, doi:10.1007/BF00993195, MR 0724699
Chan (2012). Chan, Timothy M. (2012), "Three problems about dynamic convex hulls", International Journal of Computational Geometry and Applications, 22 (4): 341–364, doi:10.1142/S0218195912600096, MR 2994585
Basch, Guibas & Hershberger (1999). Basch, Julien; Guibas, Leonidas J.; Hershberger, John (1999), "Data structures for mobile data", Journal of Algorithms, 31 (1): 1–28, doi:10.1006/jagm.1998.0988, MR 1670903
Westermann (1976). Westermann, L. R. J. (1976), "On the hull operator", Indagationes Mathematicae, 38 (2): 179–184, doi:10.1016/1385-7258(76)90065-2, MR 0404097
Herrlich (1992). Herrlich, Horst (1992), "Hyperconvex hulls of metric spaces", Proceedings of the Symposium on General Topology and Applications (Oxford, 1989), Topology and Its Applications, 44 (1–3): 181–187, doi:10.1016/0166-8641(92)90092-E, MR 1173256
Rossi (1961). Rossi, Hugo (1961), "Holomorphically convex sets in several complex variables", Annals of Mathematics, Second Series, 74 (3): 470–493, doi:10.2307/1970292, JSTOR 1970292, MR 0133479
Chazelle (1985). Chazelle, Bernard (1985), "On the convex layers of a planar set", IEEE Transactions on Information Theory, 31 (4): 509–517, Bibcode:1985ITIT...31..509C, doi:10.1109/TIT.1985.1057060, MR 0798557
Chang & Yap (1986). Chang, J. S.; Yap, C.-K. (1986), "A polynomial solution for the potato-peeling problem", Discrete & Computational Geometry, 1 (2): 155–182, doi:10.1007/BF02187692, MR 0834056
Artin (1967); Gel'fand, Kapranov & Zelevinsky (1994) Artin, Emil (1967), "2.5. Newton's Polygon", Algebraic Numbers and Algebraic Functions, Gordon and Breach, pp. 37–43, MR 0237460 Gel'fand, I. M.; Kapranov, M. M.; Zelevinsky, A. V. (1994), "6. Newton Polytopes and Chow Polytopes", Discriminants, Resultants, and Multidimensional Determinants, Mathematics: Theory & Applications, Birkhäuser, pp. 193–213, doi:10.1007/978-0-8176-4771-1, ISBN 0-8176-3660-9, MR 1264417
Prasolov (2004). Prasolov, Victor V. (2004), "1.2.1 The Gauss–Lucas theorem", Polynomials, Algorithms and Computation in Mathematics, vol. 11, Springer, pp. 12–13, doi:10.1007/978-3-642-03980-5, ISBN 3-540-40714-6, MR 2082772
Johnson (1976). Johnson, Charles R. (1976), "Normality and the numerical range", Linear Algebra and Its Applications, 15 (1): 89–94, doi:10.1016/0024-3795(76)90080-x, MR 0460358
Gardner (1984). Gardner, L. Terrell (1984), "An elementary proof of the Russo-Dye theorem", Proceedings of the American Mathematical Society, 90 (1): 171, doi:10.2307/2044692, JSTOR 2044692, MR 0722439
Reay (1979). Reay, John R. (1979), "Several generalizations of Tverberg's theorem", Israel Journal of Mathematics, 34 (3): 238–244 (1980), doi:10.1007/BF02760885, MR 0570883
Epstein & Marden (1987). Epstein, D. B. A.; Marden, A. (1987), "Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces", in Epstein, D. B. A. (ed.), Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984), London Mathematical Society Lecture Note Series, vol. 111, Cambridge: Cambridge University Press, pp. 113–253, MR 0903852
Weeks (1993). Weeks, Jeffrey R. (1993), "Convex hulls and isometries of cusped hyperbolic 3-manifolds", Topology and Its Applications, 52 (2): 127–149, doi:10.1016/0166-8641(93)90032-9, MR 1241189
Harris (1971). Harris, Bernard (1971), "Mathematical models for statistical decision theory" (PDF), Optimizing methods in statistics (Proc. Sympos., Ohio State Univ., Columbus, Ohio, 1971), pp. 369–389, MR 0356305, archived from the original (PDF) on 2021-02-28, retrieved 2020-01-01
Newton (1676); see Auel (2019), page 336, and Escobar & Kaveh (2020). Newton, Isaac (October 24, 1676), "Letter to Henry Oldenburg", The Newton Project, University of Oxford Auel, Asher (2019), "The mathematics of Grace Murray Hopper" (PDF), Notices of the American Mathematical Society, 66 (3): 330–340, doi:10.1090/noti1810, MR 3889348 Escobar, Laura; Kaveh, Kiumars (September 2020), "Convex polytopes, algebraic geometry, and combinatorics" (PDF), Notices of the American Mathematical Society, 67 (8): 1116–1123, doi:10.1090/noti2137
Dines (1938). Dines, L. L. (1938), "On convexity", American Mathematical Monthly, 45 (4): 199–209, doi:10.2307/2302604, JSTOR 2302604, MR 1524247

ams.org

Newton (1676); see Auel (2019), page 336, and Escobar & Kaveh (2020). Newton, Isaac (October 24, 1676), "Letter to Henry Oldenburg", The Newton Project, University of Oxford Auel, Asher (2019), "The mathematics of Grace Murray Hopper" (PDF), Notices of the American Mathematical Society, 66 (3): 330–340, doi:10.1090/noti1810, MR 3889348 Escobar, Laura; Kaveh, Kiumars (September 2020), "Convex polytopes, algebraic geometry, and combinatorics" (PDF), Notices of the American Mathematical Society, 67 (8): 1116–1123, doi:10.1090/noti2137

archive.org (Global: 6^th place; English: 6^th place)

Krein & Šmulian (1940), Theorem 3, pages 562–563; Schneider (1993), Theorem 1.1.2 (pages 2–3) and Chapter 3. Krein, M.; Šmulian, V. (1940), "On regularly convex sets in the space conjugate to a Banach space", Annals of Mathematics, Second Series, 41 (3): 556–583, doi:10.2307/1968735, hdl:10338.dmlcz/100106, JSTOR 1968735, MR 0002009 Schneider, Rolf (1993), Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge: Cambridge University Press, doi:10.1017/CBO9780511526282, ISBN 0-521-35220-7, MR 1216521
Gibbs (1873). Gibbs, Willard J. (1873), "A method of geometrical representation of the thermodynamic properties of substances by means of surfaces", Transactions of the Connecticut Academy of Arts and Sciences, 2: 382–404; reprinted in The Scientific Papers of J. Willard Gibbs, Vol. I: Thermodynamics, Longmans, Green, & Co., 1906, pp. 33–54

arxiv.org (Global: 49^th place; English: 31^st place)

Seaton (2017). Seaton, Katherine A. (2017), "Sphericons and D-forms: a crocheted connection", Journal of Mathematics and the Arts, 11 (4): 187–202, arXiv:1603.08409, doi:10.1080/17513472.2017.1318512, MR 3765242
Kirkpatrick (2006). Kirkpatrick, K. A. (2006), "The Schrödinger–HJW theorem", Foundations of Physics Letters, 19 (1): 95–102, arXiv:quant-ph/0305068, Bibcode:2006FoPhL..19...95K, doi:10.1007/s10702-006-1852-1

berkeley.edu (Global: 621^st place; English: 429^th place)

cnr.berkeley.edu

Getz & Wilmers (2004). Getz, Wayne M.; Wilmers, Christopher C. (2004), "A local nearest-neighbor convex-hull construction of home ranges and utilization distributions" (PDF), Ecography, 27 (4), Wiley: 489–505, Bibcode:2004Ecogr..27..489G, doi:10.1111/j.0906-7590.2004.03835.x

books.google.com (Global: 3^rd place; English: 3^rd place)

Artin (1967); Gel'fand, Kapranov & Zelevinsky (1994) Artin, Emil (1967), "2.5. Newton's Polygon", Algebraic Numbers and Algebraic Functions, Gordon and Breach, pp. 37–43, MR 0237460 Gel'fand, I. M.; Kapranov, M. M.; Zelevinsky, A. V. (1994), "6. Newton Polytopes and Chow Polytopes", Discriminants, Resultants, and Multidimensional Determinants, Mathematics: Theory & Applications, Birkhäuser, pp. 193–213, doi:10.1007/978-0-8176-4771-1, ISBN 0-8176-3660-9, MR 1264417
Prasolov (2004). Prasolov, Victor V. (2004), "1.2.1 The Gauss–Lucas theorem", Polynomials, Algorithms and Computation in Mathematics, vol. 11, Springer, pp. 12–13, doi:10.1007/978-3-642-03980-5, ISBN 3-540-40714-6, MR 2082772
Mason (1908). Mason, Herbert B. (1908), Encyclopaedia of Ships and Shipping, p. 698
Hautier (2014); Fultz (2020) Hautier, Geoffroy (2014), "Data mining approaches to high-throughput crystal structure and compound prediction", in Atahan-Evrenk, Sule; Aspuru-Guzik, Alan (eds.), Prediction and Calculation of Crystal Structures: Methods and Applications, Topics in Current Chemistry, vol. 345, Springer International Publishing, pp. 139–179, doi:10.1007/128_2013_486, ISBN 978-3-319-05773-6, PMID 24287952; see p. 143 Fultz, Brent (April 2020), Phase Transitions in Materials, Cambridge University Press, p. 55, doi:10.1017/9781108641449, ISBN 9781108641449

doi.org (Global: 2^nd place; English: 2^nd place)

Williams & Rossignac (2005). See also Douglas Zare, answer to "the perimeter of a non-convex set", MathOverflow, May 16, 2014. Williams, Jason; Rossignac, Jarek (2005), "Tightening: curvature-limiting morphological simplification", in Kobbelt, Leif; Shapiro, Vadim (eds.), Proceedings of the Tenth ACM Symposium on Solid and Physical Modeling 2005, Cambridge, Massachusetts, USA, June 13-15, 2005, ACM, pp. 107–112, doi:10.1145/1060244.1060257, hdl:1853/3736
Oberman (2007). Oberman, Adam M. (2007), "The convex envelope is the solution of a nonlinear obstacle problem", Proceedings of the American Mathematical Society, 135 (6): 1689–1694, doi:10.1090/S0002-9939-07-08887-9, MR 2286077
Knuth (1992). Knuth, Donald E. (1992), Axioms and Hulls, Lecture Notes in Computer Science, vol. 606, Heidelberg: Springer-Verlag, doi:10.1007/3-540-55611-7, ISBN 3-540-55611-7, MR 1226891, archived from the original on 2017-06-20, retrieved 2011-09-15
de Berg et al. (2008), p. 6. The idea of partitioning the hull into two chains comes from an efficient variant of Graham scan by Andrew (1979). de Berg, M.; van Kreveld, M.; Overmars, Mark; Schwarzkopf, O. (2008), Computational Geometry: Algorithms and Applications (3rd ed.), Springer Andrew, A. M. (1979), "Another efficient algorithm for convex hulls in two dimensions", Information Processing Letters, 9 (5): 216–219, doi:10.1016/0020-0190(79)90072-3
Sontag (1982). Sontag, Eduardo D. (1982), "Remarks on piecewise-linear algebra", Pacific Journal of Mathematics, 98 (1): 183–201, doi:10.2140/pjm.1982.98.183, MR 0644949
Steinitz (1914); Gustin (1947); Bárány, Katchalski & Pach (1982) Steinitz, E. (1914), "Bedingt konvergente Reihen und konvexe Systeme. (Fortsetzung)", Journal für die Reine und Angewandte Mathematik, 1914 (144): 1–40, doi:10.1515/crll.1914.144.1, MR 1580890 Gustin, William (1947), "On the interior of the convex hull of a Euclidean set", Bulletin of the American Mathematical Society, 53 (4): 299–301, doi:10.1090/S0002-9904-1947-08787-5, MR 0020800 Bárány, Imre; Katchalski, Meir; Pach, János (1982), "Quantitative Helly-type theorems", Proceedings of the American Mathematical Society, 86 (1): 109–114, doi:10.1090/S0002-9939-1982-0663877-X, JSTOR 2044407, MR 0663877
Grünbaum (2003), p. 16; Lay (1982), p. 21; Sakuma (1977). Grünbaum, Branko (2003), Convex Polytopes, Graduate Texts in Mathematics, vol. 221 (2nd ed.), Springer, ISBN 9780387004242 Lay, Steven R. (1982), Convex Sets and their Applications, John Wiley & Sons, ISBN 0-471-09584-2, MR 0655598 Sakuma, Itsuo (1977), "Closedness of convex hulls", Journal of Economic Theory, 14 (1): 223–227, doi:10.1016/0022-0531(77)90095-3
Whitley (1986). Whitley, Robert (1986), "The Kreĭn-Šmulian theorem", Proceedings of the American Mathematical Society, 97 (2): 376–377, doi:10.2307/2046536, JSTOR 2046536, MR 0835903
Krein & Milman (1940); Lay (1982), p. 43. Krein, Mark; Milman, David (1940), "On extreme points of regular convex sets", Studia Mathematica, 9: 133–138, doi:10.4064/sm-9-1-133-138 Lay, Steven R. (1982), Convex Sets and their Applications, John Wiley & Sons, ISBN 0-471-09584-2, MR 0655598
Okon (2000). Okon, T. (2000), "Choquet theory in metric spaces", Zeitschrift für Analysis und ihre Anwendungen, 19 (2): 303–314, doi:10.4171/ZAA/952, MR 1768994
Kiselman (2002). Kiselman, Christer O. (2002), "A semigroup of operators in convexity theory", Transactions of the American Mathematical Society, 354 (5): 2035–2053, doi:10.1090/S0002-9947-02-02915-X, MR 1881029
Kashiwabara, Nakamura & Okamoto (2005). Kashiwabara, Kenji; Nakamura, Masataka; Okamoto, Yoshio (2005), "The affine representation theorem for abstract convex geometries", Computational Geometry, 30 (2): 129–144, doi:10.1016/j.comgeo.2004.05.001, MR 2107032
Krein & Šmulian (1940), Theorem 3, pages 562–563; Schneider (1993), Theorem 1.1.2 (pages 2–3) and Chapter 3. Krein, M.; Šmulian, V. (1940), "On regularly convex sets in the space conjugate to a Banach space", Annals of Mathematics, Second Series, 41 (3): 556–583, doi:10.2307/1968735, hdl:10338.dmlcz/100106, JSTOR 1968735, MR 0002009 Schneider, Rolf (1993), Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge: Cambridge University Press, doi:10.1017/CBO9780511526282, ISBN 0-521-35220-7, MR 1216521
Rappoport (1992). Rappoport, Ari (1992), "An efficient adaptive algorithm for constructing the convex differences tree of a simple polygon", Computer Graphics Forum, 11 (4): 235–240, doi:10.1111/1467-8659.1140235
Demaine et al. (2008). Demaine, Erik D.; Gassend, Blaise; O'Rourke, Joseph; Toussaint, Godfried T. (2008), "All polygons flip finitely ... right?", Surveys on Discrete and Computational Geometry, Contemporary Mathematics, vol. 453, Providence, Rhode Island: American Mathematical Society, pp. 231–255, doi:10.1090/conm/453/08801, ISBN 978-0-8218-4239-3, MR 2405683
Cranston, Hsu & March (1989). Cranston, M.; Hsu, P.; March, P. (1989), "Smoothness of the convex hull of planar Brownian motion", Annals of Probability, 17 (1): 144–150, doi:10.1214/aop/1176991500, JSTOR 2244202, MR 0972777
Sedykh (1981). Sedykh, V. D. (1981), "Structure of the convex hull of a space curve", Trudy Seminara imeni I. G. Petrovskogo (6): 239–256, MR 0630708, translated in Journal of Soviet Mathematics 33 (4): 1140–1153, 1986, doi:10.1007/BF01086114
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Getz & Wilmers (2004). Getz, Wayne M.; Wilmers, Christopher C. (2004), "A local nearest-neighbor convex-hull construction of home ranges and utilization distributions" (PDF), Ecography, 27 (4), Wiley: 489–505, Bibcode:2004Ecogr..27..489G, doi:10.1111/j.0906-7590.2004.03835.x
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Hautier (2014); Fultz (2020) Hautier, Geoffroy (2014), "Data mining approaches to high-throughput crystal structure and compound prediction", in Atahan-Evrenk, Sule; Aspuru-Guzik, Alan (eds.), Prediction and Calculation of Crystal Structures: Methods and Applications, Topics in Current Chemistry, vol. 345, Springer International Publishing, pp. 139–179, doi:10.1007/128_2013_486, ISBN 978-3-319-05773-6, PMID 24287952; see p. 143 Fultz, Brent (April 2020), Phase Transitions in Materials, Cambridge University Press, p. 55, doi:10.1017/9781108641449, ISBN 9781108641449
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eudml.org (Global: low place; English: low place)

Krein & Milman (1940); Lay (1982), p. 43. Krein, Mark; Milman, David (1940), "On extreme points of regular convex sets", Studia Mathematica, 9: 133–138, doi:10.4064/sm-9-1-133-138 Lay, Steven R. (1982), Convex Sets and their Applications, John Wiley & Sons, ISBN 0-471-09584-2, MR 0655598

hdl.handle.net (Global: 66^th place; English: 34^th place)

Williams & Rossignac (2005). See also Douglas Zare, answer to "the perimeter of a non-convex set", MathOverflow, May 16, 2014. Williams, Jason; Rossignac, Jarek (2005), "Tightening: curvature-limiting morphological simplification", in Kobbelt, Leif; Shapiro, Vadim (eds.), Proceedings of the Tenth ACM Symposium on Solid and Physical Modeling 2005, Cambridge, Massachusetts, USA, June 13-15, 2005, ACM, pp. 107–112, doi:10.1145/1060244.1060257, hdl:1853/3736
Krein & Šmulian (1940), Theorem 3, pages 562–563; Schneider (1993), Theorem 1.1.2 (pages 2–3) and Chapter 3. Krein, M.; Šmulian, V. (1940), "On regularly convex sets in the space conjugate to a Banach space", Annals of Mathematics, Second Series, 41 (3): 556–583, doi:10.2307/1968735, hdl:10338.dmlcz/100106, JSTOR 1968735, MR 0002009 Schneider, Rolf (1993), Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge: Cambridge University Press, doi:10.1017/CBO9780511526282, ISBN 0-521-35220-7, MR 1216521

heldermann-verlag.de (Global: low place; English: low place)

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Steinitz (1914); Gustin (1947); Bárány, Katchalski & Pach (1982) Steinitz, E. (1914), "Bedingt konvergente Reihen und konvexe Systeme. (Fortsetzung)", Journal für die Reine und Angewandte Mathematik, 1914 (144): 1–40, doi:10.1515/crll.1914.144.1, MR 1580890 Gustin, William (1947), "On the interior of the convex hull of a Euclidean set", Bulletin of the American Mathematical Society, 53 (4): 299–301, doi:10.1090/S0002-9904-1947-08787-5, MR 0020800 Bárány, Imre; Katchalski, Meir; Pach, János (1982), "Quantitative Helly-type theorems", Proceedings of the American Mathematical Society, 86 (1): 109–114, doi:10.1090/S0002-9939-1982-0663877-X, JSTOR 2044407, MR 0663877
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Cranston, Hsu & March (1989). Cranston, M.; Hsu, P.; March, P. (1989), "Smoothness of the convex hull of planar Brownian motion", Annals of Probability, 17 (1): 144–150, doi:10.1214/aop/1176991500, JSTOR 2244202, MR 0972777
Rossi (1961). Rossi, Hugo (1961), "Holomorphically convex sets in several complex variables", Annals of Mathematics, Second Series, 74 (3): 470–493, doi:10.2307/1970292, JSTOR 1970292, MR 0133479
Gardner (1984). Gardner, L. Terrell (1984), "An elementary proof of the Russo-Dye theorem", Proceedings of the American Mathematical Society, 90 (1): 171, doi:10.2307/2044692, JSTOR 2044692, MR 0722439
Worton (1995). Worton, Bruce J. (1995), "A convex hull-based estimator of home-range size", Biometrics, 51 (4): 1206–1215, Bibcode:1995Biome..51.1206W, doi:10.2307/2533254, JSTOR 2533254
See, e.g., White (1923), page 520. White, F. Puryer (April 1923), "Pure mathematics", Science Progress in the Twentieth Century, 17 (68): 517–526, JSTOR 43432008
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mathoverflow.net (Global: low place; English: low place)

Williams & Rossignac (2005). See also Douglas Zare, answer to "the perimeter of a non-convex set", MathOverflow, May 16, 2014. Williams, Jason; Rossignac, Jarek (2005), "Tightening: curvature-limiting morphological simplification", in Kobbelt, Leif; Shapiro, Vadim (eds.), Proceedings of the Tenth ACM Symposium on Solid and Physical Modeling 2005, Cambridge, Massachusetts, USA, June 13-15, 2005, ACM, pp. 107–112, doi:10.1145/1060244.1060257, hdl:1853/3736

nih.gov (Global: 5^th place; English: 5^th place)

pubmed.ncbi.nlm.nih.gov

Kim et al. (2019). Kim, Sooran; Kim, Kyoo; Koo, Jahyun; Lee, Hoonkyung; Min, Byung Il; Kim, Duck Young (December 2019), "Pressure-induced phase transitions and superconductivity in magnesium carbides", Scientific Reports, 9 (1): 20253, Bibcode:2019NatSR...920253K, doi:10.1038/s41598-019-56497-6, PMC 6934831, PMID 31882982
Hautier (2014); Fultz (2020) Hautier, Geoffroy (2014), "Data mining approaches to high-throughput crystal structure and compound prediction", in Atahan-Evrenk, Sule; Aspuru-Guzik, Alan (eds.), Prediction and Calculation of Crystal Structures: Methods and Applications, Topics in Current Chemistry, vol. 345, Springer International Publishing, pp. 139–179, doi:10.1007/128_2013_486, ISBN 978-3-319-05773-6, PMID 24287952; see p. 143 Fultz, Brent (April 2020), Phase Transitions in Materials, Cambridge University Press, p. 55, doi:10.1017/9781108641449, ISBN 9781108641449

ncbi.nlm.nih.gov

Kim et al. (2019). Kim, Sooran; Kim, Kyoo; Koo, Jahyun; Lee, Hoonkyung; Min, Byung Il; Kim, Duck Young (December 2019), "Pressure-induced phase transitions and superconductivity in magnesium carbides", Scientific Reports, 9 (1): 20253, Bibcode:2019NatSR...920253K, doi:10.1038/s41598-019-56497-6, PMC 6934831, PMID 31882982

ox.ac.uk (Global: 541^st place; English: 356^th place)

newtonproject.ox.ac.uk

Newton (1676); see Auel (2019), page 336, and Escobar & Kaveh (2020). Newton, Isaac (October 24, 1676), "Letter to Henry Oldenburg", The Newton Project, University of Oxford Auel, Asher (2019), "The mathematics of Grace Murray Hopper" (PDF), Notices of the American Mathematical Society, 66 (3): 330–340, doi:10.1090/noti1810, MR 3889348 Escobar, Laura; Kaveh, Kiumars (September 2020), "Convex polytopes, algebraic geometry, and combinatorics" (PDF), Notices of the American Mathematical Society, 67 (8): 1116–1123, doi:10.1090/noti2137

princeton.edu (Global: 802^nd place; English: 528^th place)

cs.princeton.edu

Chazelle (1993); de Berg et al. (2008), p. 256. Chazelle, Bernard (1993), "An optimal convex hull algorithm in any fixed dimension" (PDF), Discrete & Computational Geometry, 10 (1): 377–409, doi:10.1007/BF02573985 de Berg, M.; van Kreveld, M.; Overmars, Mark; Schwarzkopf, O. (2008), Computational Geometry: Algorithms and Applications (3rd ed.), Springer

projecteuclid.org (Global: 4,781^st place; English: 3,117^th place)

Sontag (1982). Sontag, Eduardo D. (1982), "Remarks on piecewise-linear algebra", Pacific Journal of Mathematics, 98 (1): 183–201, doi:10.2140/pjm.1982.98.183, MR 0644949
This example is given by Talman (1977), Remark 2.6. Talman, Louis A. (1977), "Fixed points for condensing multifunctions in metric spaces with convex structure", Kōdai Mathematical Seminar Reports, 29 (1–2): 62–70, MR 0463985

stanford.edu (Global: 194^th place; English: 182^nd place)

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Knuth (1992). Knuth, Donald E. (1992), Axioms and Hulls, Lecture Notes in Computer Science, vol. 606, Heidelberg: Springer-Verlag, doi:10.1007/3-540-55611-7, ISBN 3-540-55611-7, MR 1226891, archived from the original on 2017-06-20, retrieved 2011-09-15

web.archive.org (Global: 1^st place; English: 1^st place)

Knuth (1992). Knuth, Donald E. (1992), Axioms and Hulls, Lecture Notes in Computer Science, vol. 606, Heidelberg: Springer-Verlag, doi:10.1007/3-540-55611-7, ISBN 3-540-55611-7, MR 1226891, archived from the original on 2017-06-20, retrieved 2011-09-15
Harris (1971). Harris, Bernard (1971), "Mathematical models for statistical decision theory" (PDF), Optimizing methods in statistics (Proc. Sympos., Ohio State Univ., Columbus, Ohio, 1971), pp. 369–389, MR 0356305, archived from the original (PDF) on 2021-02-28, retrieved 2020-01-01

Convex hull (English Wikipedia)

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