Stable constant mean curvature surfaces minimize area

Karsten Große-Brauckmann

Vol. 175 (1996), No. 2, 527–534

DOI: 10.2140/pjm.1996.175.527

Abstract

Let M be an embedded strictly stable constant mean curvature surface, and S a surface with the same boundary that encloses the same volume. If S is sufficiently close to M we show area(S) > area(M) unless S = M, i.e. M is a local minimum of area.

Mathematical Subject Classification 2000

Primary: 53A10

Secondary: 49Q05, 58E12, 49Q25

Milestones

Published: 1 October 1996