8 papers
Alexandrov--Fenchel inequalities for closed axisymmetric hypersurfaces
Weimin Sheng, Yinhang Wang
We establish sharp Alexandrov--Fenchel inequalities for closed, embedded, axisymmetric hypersurfaces Sigma in n+1 dimensional Euclidean space R^{n+1}, the dimension n > or = 2, wit…
Supercritical dual k-Minkowski flows with general prescribed data: a priori estimates and asymptotic convergence
Hongyi Sheng, Weimin Sheng, Jiazhuo Yang
Let k be an integer from 1 to n, let f be a positive smooth function on the unit sphere, and consider the normalized flow X_t = -f({nu})|X|^{alpha} sigma_k({kappa}) {nu} + beta X,…
Non-homogeneous curvature flows in a hemisphere
Hongyi Sheng, Weimin Sheng, Jiazhuo Yang
Let S^{n+1}_{+} be the open hemisphere of the unit sphere S^{n+1} centred at o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^{alpha} {nu} of smooth, closed, strict…
Non-homogeneous curvature flows in hyperbolic space
Hongyi Sheng, Weimin Sheng, Jiazhuo Yang
Let H^{n+1} be hyperbolic space of sectional curvature -1, with a fixed point o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^{alpha} {nu} of smooth, closed, stric…
Noncollapsing for Curvature Flows with Inhomogeneous Speeds
Weimin Sheng, Ye Zhu
We study closed, embedded hypersurfaces in Euclidean space evolving by fully nonlinear curvature flows, whose speed is given by a symmetric, monotone increasing, -homogeneous, p…
Long time behavior of a class of non-homogeneous anisotropic fully nonlinear curvature flows
Weimin Sheng, Jiazhuo Yang
In this paper, we study a class of non-homogeneous anisotropic fully nonlinear curvature flows in . More precisely, we consider a hypersurface in $\mathbb{R}^…
On the new weighted geometric inequalities near the sphere in space forms
Weimin Sheng, Yinhang Wang
In this paper, we first investigate weighted Minkowski type inequalities for nearly spherical sets in space forms, focusing on the sets that are -close to geodesic spheres. Ou…
On rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space
Weimin Sheng, Yinhang Wang, Jie Wu
In this paper, we first give some new characterizations of geodesic spheres in the hyperbolic space by the condition that hypersurface has constant weighted shifted mean curvatures…