9 papers
Alexandrov--Fenchel inequalities for convex domains in the sphere
Tianci Luo, Yong Wei, Rong Zhou
We prove the Alexandrov--Fenchel inequalities between any two spherical quermassintegrals for smooth weakly convex domains contained in an open hemisphere, with equality if and onl…
Positive -bi-Ricci curvature and Mean curvature flow with surgery in hyperbolic space
Tianci Luo, Yong Wei, Rong Zhou
Let and . We prove that every smooth closed connected immersed hypersurface in hyperbolic space whose induced metric has positive -bi-Ricci curvature admit…
Weinstock inequalities for outward-minimizing domains
Chaoqun Gao, Yong Wei, Rong Zhou
We prove sharp Weinstock inequalities for the first nonzero Steklov eigenvalue of smooth outward-minimizing domains in Euclidean space and hyperbolic space. The method is based on…
Free boundary flows by powers of the Gauss curvature in the unit ball
Tianci Luo, Yong Wei, Rong Zhou
We study smooth compact strictly convex hypersurfaces in the unit ball that meet the support sphere orthogonally and evolve by the -Gauss curvature flow , $α>…
Higher regularity of the inverse anisotropic mean curvature flow
Chaoqun Gao, Yong Wei, Rong Zhou
We prove an anisotropic analogue of the higher regularity theorem of Huisken and Ilmanen for inverse mean curvature flow. For an arbitrary smooth Minkowski norm, we first prove a H…
Contraction of hypersurfaces with positive sectional curvature in hyperbolic space
Tianci Luo, Yong Wei, Rong Zhou
We study contracting curvature flows of compact hypersurfaces with positive sectional curvature in hyperbolic space . The speed is assumed to be homogeneous of de…
Asymptotic behaviour of the weak inverse anisotropic mean curvature flow
Chaoqun Gao, Yong Wei, Rong Zhou
We first establish a local gradient estimate for anisotropic -harmonic functions. A key feature of our estimate is that the constant remains bounded as ; consequently, i…
Geometric inequalities and their stabilities for modified quermassintegrals in hyperbolic space
Chaoqun Gao, Rong Zhou
In this paper, we first consider the curve case of Hu-Li-Wei's flow for shifted principal curvatures of h-convex hypersurfaces in proposed in [10]. We prove that…
Gauss curvature type flow and Alexandrov-Fenchel inequalities in the hyperbolic space
Tianci Luo, Rong Zhou
We consider the Gauss curvature type flow for uniformly convex hypersurfaces in the hyperbolic space . We prove that if the initial closed hypersu…