Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Xiong, Changwei"'
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 $\mathbb{B}^n_1\setminus \overline{\mathbb{B}^n_\epsilon}$ as $\epsilon \to
Externí odkaz:
http://arxiv.org/abs/2410.20805
Autor:
Xiong, Changwei
First we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary. Then we give two applications of this formula when the manifold satisfies certain geometric conditions. One is a sharp
Externí odkaz:
http://arxiv.org/abs/2312.16780
We derive various sharp upper bounds for the $p$-capacity of a smooth compact set $K$ in the hyperbolic space $\mathbb{H}^n$ and the Euclidean space $\mathbb{R}^n$. Firstly, using the inverse mean curvature flow, for the mean convex and star-shaped s
Externí odkaz:
http://arxiv.org/abs/2306.09009
Autor:
Xiong, Changwei
Let $U\subset \mathbb{R}^n$ ($n\geq 3$) be an exterior Euclidean domain with smooth boundary $\partial U$. We consider the Steklov eigenvalue problem on $U$. First we derive a sharp lower bound for the first eigenvalue in terms of the support functio
Externí odkaz:
http://arxiv.org/abs/2304.11297
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 anisotropic curvature measure equals a linear combination of other low
Externí odkaz:
http://arxiv.org/abs/2108.02049
Publikováno v:
In Journal of Radiation Research and Applied Sciences March 2024 17(1)
Autor:
Li, Ruixuan, Xiong, Changwei
We prove various sharp bounds for the anisotropic $p$-capacity $\mathrm{Cap}_{F,p}(K)$ ($1
Externí odkaz:
http://arxiv.org/abs/2104.09905
Autor:
Wei, Yong, Xiong, Changwei
Publikováno v:
Nonlinear Analysis, vol. 217, April 2022, 112760
Given a smooth positive function $F\in C^{\infty}(\mathbb{S}^n)$ such that the square of its positive $1$-homogeneous extension on $\mathbb{R}^{n+1}\setminus \{0\}$ is uniformly convex, the Wulff shape $W_F$ is a smooth uniformly convex body in the E
Externí odkaz:
http://arxiv.org/abs/2103.16088
Autor:
Xia, Chao, Xiong, Changwei
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 Ricci curvature and boundary principal curvatures bounded below by $c
Externí odkaz:
http://arxiv.org/abs/1907.07340
Autor:
Xiong, Changwei
Let $M^n=[0,R)\times \mathbb{S}^{n-1}$ be an $n$-dimensional ($n\geq 2$) smooth Riemannian manifold equipped with the warped product metric $g=dr^2+h^2(r)g_{\mathbb{S}^{n-1}}$ and diffeomorphic to a Euclidean ball. Assume that $M$ has strictly convex
Externí odkaz:
http://arxiv.org/abs/1902.00656