6 papers · 1 filter
Sharp stability for mixed bubbles on hyperbolic space
Juncheng Wei, Zetian Yan, Zhipeng Yang
We prove sharp residual stability estimates for the critical Poincaré-Sobolev equation near sums of one positive hyperbolic solution and one projected Euclidean bubble in dimension…
On Dolbeault's conjecture
Juncheng Wei, Zetian Yan, Zikai Ye
We prove sharp improved Sobolev inequalities on , , for antipodally even functions and for axially symmetric functions whose critical density h…
Prüfer -group and Milnor's Conjecture on Fundamental Groups
Nan Wu, Zetian Yan
We construct complete, one-ended Riemannian manifolds in dimensions four and five having strictly positive Ricci curvature, with fundamental group isomorphic to the Prüfer -grou…
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…