Changwei Xiong

activity

20122025

most citedA geometric inequality on hypersurface in hyperbolic space

68 citations · 160 across the 20 of their papers we have counts for

collaborators

20 papers

math.DG2025

Scaling inequalities for Steklov eigenvalues in space forms and sharp eigenvalue estimates on warped product manifolds

Zongyi Lv, Changwei Xiong, Yuxun Zou

In the first part, we derive monotonicity of the normalized spectra for the second-order Steklov problem and two fourth-order Steklov problems on the $2$ -dimensional geodesic disks…

math.AP2024

On shape optimization for fourth order Steklov eigenvalue problems

Changwei Xiong, Jinglong Yang, Jinchao Yu

We study three types of fourth-order Steklov eigenvalue problems. For the first two of them, we derive the asymptotic expansion of their spectra on Euclidean annular domains $\math…

math.DG2023

Sharp upper bounds for the capacity in the hyperbolic and Euclidean spaces

Haizhong Li, Ruixuan Li, Changwei Xiong

We derive various sharp upper bounds for the $p$ -capacity of a smooth compact set $K$ in the hyperbolic space $H^{n}$ and the Euclidean space $R^{n}$ . Firstly, using…

math.AP2023★ 1 cited

Sharp bounds for the first two eigenvalues of an exterior Steklov eigenvalue problem

Changwei Xiong

Let $U \subset R^{n}$ ( $n \geq 3$ ) be an exterior Euclidean domain with smooth boundary $\partial U$ . We consider the Steklov eigenvalue problem on $U$ . First we derive a shar…

math.DG2021

Anisotropic curvature measures and volume preserving flows

Ben Andrews, Yitao Lei, Yong Wei +1

In the first part of this paper, we develop the theory of anisotropic curvature measures for convex bodies in the Euclidean space. It is proved that any convex body whose boundary…

math.DG2021

Sharp bounds for the anisotropic $p$ -capacity of Euclidean compact sets

Ruixuan Li, Changwei Xiong

We prove various sharp bounds for the anisotropic $p$ -capacity $Cap_{F, p} (K)$ ( $1 < p < n$ ) of compact sets $K$ in the Euclidean space $R^{n}$ ( $n \geq 3$ ). For example,…

math.DG2021★ 10 cited

A fully nonlinear locally constrained anisotropic curvature flow

Yong Wei, Changwei Xiong

Given a smooth positive function $F \in C^{\infty} (S^{n})$ such that the square of its positive $1$ -homogeneous extension on $R^{n + 1} ∖ {0}$ is uniformly co…

math.DG2019★ 5 cited

Escobar's Conjecture on a sharp lower bound for the first nonzero Steklov eigenvalue

Chao Xia, Changwei Xiong

It was conjectured by Escobar [J. Funct. Anal. 165 (1999), 101--116] that for an $n$ -dimensional ( $n \geq 3$ ) smooth compact Riemannian manifold with boundary, which has nonnegative…

math.DG2019

On the spectra of three Steklov eigenvalue problems on warped product manifolds

Changwei Xiong

Let $M^{n} = [0, R) \times S^{n - 1}$ be an $n$ -dimensional ( $n \geq 2$ ) smooth Riemannian manifold equipped with the warped product metric $g = d r^{2} + h^{2} (r) g_{S^{n - 1}}$ and…

math.DG2018

Homotopy type of manifolds with partially horoconvex boundary

Changwei Xiong

Let $M$ be an $n$ -dimensional compact connected manifold with boundary, $κ > 0$ a constant and $1 \leq q \leq n - 1$ an integer. We prove that $M$ supports a Riemannian metric with the i…

math.DG2018★ 11 cited

Gradient estimates via two-point functions for elliptic equations on manifolds

Ben Andrews, Changwei Xiong

We derive estimates relating the values of a solution at any two points to the distance between the points, for quasilinear isotropic elliptic equations on compact Riemannian manif…

math.DG2017★ 1 cited

Nonnegatively curved hypersurfaces with free boundary on a sphere

Mohammad Ghomi, Changwei Xiong

We prove that in Euclidean space $R^{n + 1}$ any compact immersed nonnegatively curved hypersurface $M$ with free boundary on the sphere $S^{n}$ is an embedded convex topological disk.…

math.DG2017★ 5 cited

Comparison of Steklov eigenvalues on a domain and Laplacian eigenvalues on its boundary in Riemannian manifolds

Changwei Xiong

We prove that in Riemannian manifolds the $k$ -th Steklov eigenvalue on a domain and the square root of the $k$ -th Laplacian eigenvalue on its boundary can be mutually controlled in…

math.DG2017★ 1 cited

A gap theorem for free boundary minimal surfaces in geodesic balls of hyperbolic space and hemisphere

Haizhong Li, Changwei Xiong

In this paper we provide a pinching condition for the characterization of the totally geodesic disk and the rotational annulus among minimal surfaces with free boundary in geodesic…

math.DG2014★ 14 cited

Stability of capillary hypersurfaces in a Euclidean ball

Haizhong Li, Changwei Xiong

We study the stability of capillary hypersurfaces in a unit Euclidean ball. It is proved that if the mass center of the generalized body enclosed by the immersed capillary hypersur…

math.DG2013★ 23 cited

Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere

Yong Wei, Changwei Xiong

In this paper, firstly, inspired by Natário's recent work \cite{Na}, we use the isoperimetric inequality to derive some Alexandrov-Fenchel type inequalities for closed convex hyper…

math.DG2013★ 11 cited

The Gauss-Bonnet-Chern mass for graphic manifolds

Haizhong Li, Yong Wei, Changwei Xiong

In this paper, we prove a positive mass theorem and Penrose-type inequality of the Gauss-Bonnet-Chern mass $m_{2}$ for the graphic manifold with flat normal bundle.

math.DG2013★ 1 cited

Hypersurfaces with constant anisotropic mean curvatures

Hui Ma, Changwei Xiong

We apply the evolution method to present a new proof of the Alexandrov type theorem for constant anisotropic mean curvature hypersurfaces in the Euclidean space $R^{n + 1}$ .

math.DG2012★ 68 cited

A geometric inequality on hypersurface in hyperbolic space

Haizhong Li, Yong Wei, Changwei Xiong

In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.

math.DG2012★ 9 cited

Note on Brendle-Eichmair's paper "Isoperimetric and Weingarten surfaces in the Schwarchild manifold"

Haizhong Li, Yong Wei, Changwei Xiong

In this short note, we show that the assumption "convex" in Theorem 7 of Brendle-Eichmair's paper \cite{BE} is unnecessary.

Scaling inequalities for Steklov eigenvalues in space forms and sharp eigenvalue estimates on warped product manifolds

On shape optimization for fourth order Steklov eigenvalue problems

Sharp upper bounds for the capacity in the hyperbolic and Euclidean spaces

Sharp bounds for the first two eigenvalues of an exterior Steklov eigenvalue problem

Anisotropic curvature measures and volume preserving flows

Sharp bounds for the anisotropic p-capacity of Euclidean compact sets

A fully nonlinear locally constrained anisotropic curvature flow

Escobar's Conjecture on a sharp lower bound for the first nonzero Steklov eigenvalue

On the spectra of three Steklov eigenvalue problems on warped product manifolds

Homotopy type of manifolds with partially horoconvex boundary

Gradient estimates via two-point functions for elliptic equations on manifolds

Nonnegatively curved hypersurfaces with free boundary on a sphere

Comparison of Steklov eigenvalues on a domain and Laplacian eigenvalues on its boundary in Riemannian manifolds

A gap theorem for free boundary minimal surfaces in geodesic balls of hyperbolic space and hemisphere

Stability of capillary hypersurfaces in a Euclidean ball

Alexandrov-Fenchel type inequalities for convex hypersurfaces in hyperbolic space and in sphere

The Gauss-Bonnet-Chern mass for graphic manifolds

Hypersurfaces with constant anisotropic mean curvatures

A geometric inequality on hypersurface in hyperbolic space

Note on Brendle-Eichmair's paper "Isoperimetric and Weingarten surfaces in the Schwarchild manifold"

Sharp bounds for the anisotropic $p$ -capacity of Euclidean compact sets