53 citations · 84 across the 16 of their papers we have counts for
15 papers · 1 filter
Affine isoperimetric type inequalities for static convex domains in hyperbolic space
Yingxiang Hu, Haizhong Li, Yao Wan +1
In this paper, the notion of hyperbolic ellipsoids in hyperbolic space is introduced. Using a natural orthogonal projection from hyperbolic space to Euclidean space, we establish a…
The horospherical -Christoffel-Minkowski and prescribed -shifted Weingarten curvature problems in hyperbolic space
Yingxiang Hu, Haizhong Li, Botong Xu
The -Christoffel-Minkowski problem and the prescribed -Weingarten curvature problem for convex hypersurfaces in Euclidean space are important problems in geometric analys…
A Heintze-Karcher type inequality in hyperbolic space
Yingxiang Hu, Yong Wei, Tailong Zhou
In this paper, we prove a new Heintze-Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov type theorem for cl…
On the mean curvature type flow for convex capillary hypersurfaces in the ball
Yingxiang Hu, Yong Wei, Bo Yang +1
In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang-Xia and Wang-Weng. We show t…
Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms
Yingxiang Hu, Haizhong Li
In this paper, we prove a family of identities for closed and strictly convex hypersurfaces in the sphere and hyperbolic/de Sitter space. As applications, we prove Blaschke-Santaló…
Geometric inequalities for free boundary hypersurfaces in a ball
Yimin Chen, Yingxiang Hu, Haizhong Li
In this paper, we prove a family of sharp geometric inequalities for free boundary hypersurfaces in a ball in space forms.
Geometric inequalities for static convex domains in hyperbolic space
Yingxiang Hu, Haizhong Li
We prove that the static convexity is preserved along two kinds of locally constrained curvature flows in hyperbolic space. Using the static convexity of the flow hypersurfaces, we…
Locally constrained curvature flows and geometric inequalities in hyperbolic space
Yingxiang Hu, Haizhong Li, Yong Wei
In this paper, we first study the locally constrained curvature flow of hypersurfaces in hyperbolic space, which was introduced by Brendle, Guan and Li [7]. This flow preserves the…
1st eigenvalue pinching for convex hypersurfaces in a Riemannian manifold
Yingxiang Hu, Shicheng Xu
Let be a closed convex hypersurface lying in a convex ball of the ambient -manifold . We prove that, by pinching Heintze-Reilly's inequality via sect…
Recognizing shape via 1st eigenvalue, mean curvature and upper curvature bound
Yingxiang Hu, Shicheng Xu
Let be a closed immersed hypersurface lying in a contractible ball of the ambient -manifold . We prove that, by pinching Heintze-Reilly's inequality…
Contraction of surfaces in hyperbolic space and in sphere
Yingxiang Hu, Haizhong Li, Yong Wei +1
In this paper, we consider the contracting curvature flow of smooth closed surfaces in -dimensional hyperbolic space and in -dimensional sphere. In the hyperbolic case, we sh…
Harmonic mean curvature flow and geometric inequalities
Ben Andrews, Yingxiang Hu, Haizhong Li
In this article, we will use the harmonic mean curvature flow to prove a new class of Alexandrov-Fenchel type inequalities for strictly convex hypersurfaces in hyperbolic space in…
Geometric inequalities for hypersurfaces with nonnegative sectional curvature in hyperbolic space
Yingxiang Hu, Haizhong Li
In this article, we will use inverse mean curvature flow to establish an optimal Sobolev-type inequality for hypersurfaces with nonnegative sectional curvature in $\mathbb{H}^n…
Willmore inequality on hypersurfaces in hyperbolic space
Yingxiang Hu
In this article, we prove a geometric inequality for star-shaped and mean-convex hypersurfaces in hyperbolic space by inverse mean curvature flow. This inequality can be considered…
An Eigenvalue Pinching Theorem for Compact Hypersurfaces in A Sphere
Yingxiang Hu, Hongwei Xu
In this article, we prove an eigenvalue pinching theorem for the first eigenvalue of the Laplacian on compact hypersurfaces in a sphere. Let be a closed, connected and or…