Stability of hypersurfaces of constant mean curvature with free boundary in two parallel hyperplanes

被引：0

作者：

Koiso, Miyuki ^{[1
]}

Miyamoto, Umpei ^{[2
]}

机构：

[1] Kyushu Univ, Inst Math Ind, 744 Motooka,Nishi Ku, Fukuoka 8190395, Japan

[2] Akita Prefectural Univ, Res & Educ Ctr Comprehens Sci, 84-4 Aza Ebinokuchi, Tsuchiya, Akita 0150055, Japan

来源：

JSIAM LETTERS | 2023年 / 15卷

关键词：

constant mean curvature surface; Delaunay surface; unduloid; variational prob-lem; stability; SURFACES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Surfaces with constant mean curvature (CMC) are critical points of the area with volume constraint. They serve as a mathematical model of surfaces of soap bubbles and tiny liquid drops. CMC surfaces are said to be stable if the second variation of the area is nonnegative for all volume-preserving variations satisfying the given boundary condition. In this paper, we examine the stability of CMC hypersurfaces in general Euclidean space possibly having boundaries on two parallel hyperplanes. We reveal the stability of equilibrium hypersurfaces without self-intersection for the first time in all dimensions. The analysis is assisted by nu-merical computations.

引用

页码：9 / 12

页数：4

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