The maximum diam theorem on Finsler manifolds
Differential Geometry
2018-01-16 v1
Abstract
We prove that, for a Finsler space, if the weighted Ricci curvature is bounded below by a positive number and the diam attains its maximal value, then it is isometric to a standard Finsler sphere. As an application, we show that the first eigenvalue of the Finsler-Laplacian attains its lower bound if and only if the Finsler manifold is isometric to a standard Finsler sphere, and moreover, we obtain an explicit 1-st eigenfunction on the sphere.
Keywords
Cite
@article{arxiv.1801.04527,
title = {The maximum diam theorem on Finsler manifolds},
author = {Songting Yin and Qun He},
journal= {arXiv preprint arXiv:1801.04527},
year = {2018}
}
Comments
15 pages. No figure