13 papers
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…
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…
Energy reduction for Fourth order Willmore energy
Nan Wu, Zetian Yan
We introduce a fourth-order Willmore-type problem for closed four-dimensional submanifolds immersed in and establish a connected sum energy reduction for the general…
Juhl type formulas for curved Ovsienko--Redou operators
Shane Chern, Zetian Yan
We prove Juhl type formulas for the curved Ovsienko--Redou operators and their linear analogues, which indicate the associated formal self-adjointness, thereby confirming two conje…
Formal self-adjointness of a family of conformally invariant bidifferential operators
Jeffrey S. Case, Zetian Yan
We prove that the curved Ovsienko--Redou operators and a related family of differential operators are formally self-adjoint. This verifies two conjectures of Case, Lin, and Yuan.
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…
Stable free boundary minimal hypersurfaces in locally wedge-shaped manifolds
Zetian Yan
We prove that a stable -to-edge properly embedded free boundary minimal hypersurface of a -dimensional wedge domain with angle is flat.