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Rigidity and Classification of Manifolds with Maximal Boundary Static Kernels
Hongyi Sheng, Caihong Yi
Boundary static potentials arise from the adjoint equations associated with simultaneous variations of scalar curvature and boundary mean curvature. On a connected manifold of dime…
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…