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math.AP2025
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…
math.DG2025
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…
math.DG2025
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…