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arXiv · 2111.02289

Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space

Jinyu Guo·Guofang Wang·Chao Xia
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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.

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Jinyu Guo, Guofang Wang, Chao Xia. 2021-11-03. Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space. https://arxiv.org/abs/2111.02289

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