See (Nishikawa 2002) about variational definition. Nishikawa, Seiki (2002). Variational problems in geometry. Translations of mathematical monographs; Iwanami series in modern mathematics. Vol. 205. Translated by Abe, Kinetsu. Providence, R. I. : American Mathematical Society. ISBN0821813560. ISSN0065-9282, translated from:{{cite book}}: CS1 maint: postscript (link)