4 papers
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…
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…
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…
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…