9 papers
Nonnegative Ricci Curvature and Uniformly Convex Boundary Forces Compactness
Zetian Yan, Xingyu Zhu
We confirm a compactness conjecture of M. Li. If a complete Riemannian manifold has nonnegative Ricci curvature and uniformly convex boundary in the sense that the second fundament…
Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions
Zetian Yan, Xingyu Zhu
We study complete -manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R…
Uniqueness of the asymptotic limits for Ricci-flat manifolds with linear volume growth II
Zetian Yan, Xingyu Zhu
We relate the uniqueness of asymptotic limits for noncollapsed Ricci flat manifolds with linear volume growth to the existence of a harmonic function asymptotic to a Busemann funct…
Sharp Fractional Sobolev Embeddings on Closed Manifolds
Hao Tan, Zetian Yan, Zhipeng Yang
We develop an intrinsic, heat-kernel based fractional Sobolev framework on closed Riemannian manifolds and study the critical fractional Sobolev embedding. We determine the optimal…
Uniqueness of the asymptotic limits for Ricci-flat manifolds with linear volume growth
Zetian Yan, Xingyu Zhu
Under natural assumptions on curvature and cross section, we establish the uniqueness of asymptotic limits and the exponential convergence rate for complete noncollapsed Ricci-flat…
Rigidity of CMC hypersurfaces in 5-and 6-manifolds
Han Hong, Zetian Yan
We prove that nonnegative -intermediate Ricci curvature combined with uniformly positive -triRic curvature implies rigidity of complete noncompact two-sided stable minimal hy…