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math.DG2021
Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space
Jinyu Guo, Guofang Wang, Chao Xia
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 umbi…
math.DG2021
Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
Liangjun Weng, Chao Xia
In this paper, we first introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball and derive its first variatio…
math.DG2021
Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
Chao Xia, Xuwen Zhang
In this paper, we prove a Poincaré-type inequality for any set of finite perimeter which is stable with respect to the free energy among volume-preserving perturbation, provided th…