1 citations · 1 across the 4 of their papers we have counts for
7 papers
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…
Obata-Type Rigidity on Static Manifolds with Boundary
Hongyi Sheng, Kai-Wei Zhao
We investigate static metrics on simple manifolds with compact boundary and establish an Obata-type rigidity theorem. We identify new sufficient geometric conditions under which th…
Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature
Jiashu Shen, Hongyi Sheng
Let be a compact Riemannian manifold with boundary . Given a function on , we consider the problem of finding a conformal metric of with ze…
Static Manifolds with Boundary and Rigidity of Scalar Curvature and Mean Curvature
Hongyi Sheng
On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. Mor…
Localized Deformation of the Scalar Curvature and the Mean Curvature
Hongyi Sheng
On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. We…