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math.SP2024
The first Neumann eigenvalue and the width
Haibin Wang, Guoyi Xu
We prove the sharp lower bound of the first Neumann eigenvalue for bounded convex planar domain in term of its diameter and width.
math.DG2024
The first Dirichlet eigenvalue and the width
Guoyi Xu
For a geodesic ball with non-negative Ricci curvature and mean convex boundary, it is known that the first Dirichlet eigenvalue of this geodesic ball has a sharp lower bound in ter…
math.DG2024
The rigidity of eigenfunctions' gradient estimates
Guoyi Xu, Xiaolong Xue
On compact Riemannian manifolds with non-negative Ricci curvature and smooth (possibly empty), convex (or mean convex) boundary, if the sharp Li-Yau type gradient estimate of an Ne…