A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms

Autor:	Mei, Xinqun, Weng, Liangjun
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs 53C44 (Primary) 35K93 (Secondary)
Zdroj:	J. Geom. Anal. 33 (2023), no. 6, Paper No. 195, 28 pp
Druh dokumentu:	Working Paper
DOI:	10.1007/s12220-023-01255-4
Popis:	In this paper, we introduce a new constrained mean curvature type flow for capillary boundary hypersurfaces in space forms. We show the flow exists for all time and converges globally to a spherical cap. Moreover, the flow preserves the volume of the bounded domain enclosed by the hypersurface and decreases the total energy. As a by-product, we give a flow proof of the capillary isoperimetric inequality for the starshaped capillary boundary hypersurfaces in space forms. Comment: 23pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.07651 Zobrazit plný text záznamu View this record from Arxiv