Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space
Differential Geometry
2021-11-04 v1
Abstract
In this paper, we study a stability problem of free boundary hypersurfaces, and also capillary ones whose boundary supported on a horosphere in hyperbolic space. We prove that umbilical hypersurfaces are only stable immersed capillary hypersurfaces whose boundary supported on a horosphere. Using the same method, we show that a totally geodesic hyperplane is only stable immersed type-II hypersurface whose boundary supported on a horosphere.
Keywords
Cite
@article{arxiv.2111.02289,
title = {Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space},
author = {Jinyu Guo and Guofang Wang and Chao Xia},
journal= {arXiv preprint arXiv:2111.02289},
year = {2021}
}
Comments
16 pages,1 figure