A rigidity result of spectral gap on Finsler manifolds and its application

2022/04/05 by Mai, Cong Hung
#53B40 #53C24 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.02298

Abstract

We investigate the rigidity problem for the sharp spectral gap on Finsler manifolds of weighted Ricci curvature bound Ric_∞ ≥ K > 0. Our main results show that if the equality holds, the manifold necessarily admits a diffeomorphic splitting (or isometric splitting in the particular class of Berwald spaces). This splitting phenomenon is comparable to the Cheeger-Gromoll type splitting theorem by Ohta. We also obtain the rigidity results of logarithmic Sobolev and Bakry-Ledoux isoperimetric inequalities via needle decomposition as corollaries.

Related

• Rigidity for the spectral gap on RCD(K,∞)-spaces
• Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature
• Sharp Hardy and spectral gap inequalities on special irreversible Finsler manifolds
• Spectral rigidity of manifolds with Ricci bounded below and maximal bottom spectrum
• Sharp Spectral Gap Estimates on Manifolds under Integral Ricci Curvature Bounds