26 citations · 177 across the 51 of their papers we have counts for
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A Sharp Diameter-Dependent Lower Bound for the First Nonzero Neumann Eigenvalue of Geodesic Triangles in Space Forms
Shoo Seto, Guofang Wei, Yusen Xia
We prove a sharp lower bound for the first nonzero Neumann eigenvalue of geodesic triangles of given diameter in two-dimensional space forms. The bound is given by the first positi…
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…
Finite Diffeomorphism Theorem for manifolds with lower Ricci curvature and bounded energy
Wenshuai Jiang, Guofang Wei
In this paper we prove that the space $\cM(n,\rv,D,Λ):=\{(M^n,g) \text{ closed }: ~~\Ric\ge -(n-1),~\Vol(M)\ge \rv>0, \diam(M)\le D \text{ and } \int_{M}|\Rm|^{n/2}\le Λ\}$ has at…
Modulus of Concavity and Fundamental Gap Estimates on Surfaces
Gabriel Khan, Malik Tuerkoen, Guofang Wei
The fundamental gap of a domain is the difference between the first two eigenvalues of the Laplace operator. In a series of recent and celebrated works, it was shown that for conve…
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…
Singular Weyl's law with Ricci curvature bounded below
Xianzhe Dai, Shouhei Honda, Jiayin Pan +1
We establish two surprising types of Weyl's laws for some compact /Ricci limit spaces. The first type could have power growth of any order (bigger than one). Th…