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math.DG2026
Fenchel-Willmore-Chen inequality under lower bounds on weighted intermediate Ricci curvature
Jihye Lee, Guofang Wei
We establish a Fenchel-Willmore-Chen inequality for smooth metric measure spaces with a lower bound on the 1-Bakry-Emery k-Ricci curvature. This extends previous results and yields…
math.DG2024
Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature
Gabriel Khan, Xuan Hien Nguyen, Malik Tuerkoen +1
We study the log-concavity of the first Dirichlet eigenfunction of the Laplacian for convex domains. For positively curved surfaces satisfying a condition involving the curvature a…
math.DG2024
Finite Diffeomorphism Theorem for manifolds with lower Ricci curvature and bounded energy
Wenshuai Jiang, Guofang Wei
In this paper we prove that the space $\cM(n,\rv,D,Î):=\{(M^n,g) \text{ closed }: ~~\Ric\ge -(n-1),~\Vol(M)\ge \rv>0, \diam(M)\le D \text{ and } \int_{M}|\Rm|^{n/2}\le Î\}$ has a…