Capillary hypersurfaces, Heintze-Karcher's inequality and Zermelo's navigation
Differential Geometry
2024-01-17 v1
Abstract
In this paper, we establish a Heintze-Karcher-type inequality for capillary hypersurfaces in a unit ball. To achieve this, we introduce a special Finsler metric given by Zermelo's navigation and study the geodesic normal flow with respect to this Finsler metric. Our results indicate that the relationship between capillary hypersufaces and hypersurfaces with free boundary is similar to the one between Finsler geometry and Riemannian geometry.
Keywords
Cite
@article{arxiv.2401.08450,
title = {Capillary hypersurfaces, Heintze-Karcher's inequality and Zermelo's navigation},
author = {Guofang Wang and Chao Xia},
journal= {arXiv preprint arXiv:2401.08450},
year = {2024}
}
Comments
18 pages