A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
Differential Geometry
2024-09-02 v1 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.2302.07651,
title = {A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms},
author = {Xinqun Mei and Liangjun Weng},
journal= {arXiv preprint arXiv:2302.07651},
year = {2024}
}
Comments
23pages