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

Autor:	Koiso, Miyuki, Miyamoto, Umpei
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematical Physics
Zdroj:	JSIAM Letters, vol. 15, pp. 9-12 (2023)
Druh dokumentu:	Working Paper
DOI:	10.14495/jsiaml.15.9
Popis:	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 numerical computations. Comment: 4 pages, 3 figures, 3 tables, a letter version of full paper arXiv:1905.01705
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.12211 Zobrazit plný text záznamu View this record from Arxiv