26 citations · 177 across the 51 of their papers we have counts for
4 papers · 2 filters
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…
Ricci Flow and Gromov Almost Flat Manifolds
Eric Chen, Guofang Wei, Rugang Ye
We employ the Ricci flow to derive a new theorem about Gromov almost flat manifolds, which generalizes and strengthens the celebrated Gromov--Ruh Theorem. In our theorem, the condi…
Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions
Jiayin Pan, Guofang Wei
We give the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function at a point. This provides counterexamples to a longtime well-known op…