2021 Fiscal Year Annual Research Report

Geometric analysis and comparison geometry on weighted manifolds

Research Project

Project/Area Number	20J11328
Research Institution	Osaka University
Principal Investigator	Mai Cong Hung 大阪大学, 理学研究科, 特別研究員(PD)
Project Period (FY)	2020-04-24 – 2022-03-31
Keywords	Finsler manifolds / Berwald spaces / diffeomorphic splitting / rigidity / Bakry-Ledoux inequality / log sobolev / needle decomposition
Outline of Annual Research Achievements	During this research period, I study the studies on the rigidity of sharp spectral gaps in the setting of Finsler manifolds. I investigated the rigidity problem for the sharp spectral gap on Finsler manifolds and obtained the diffeomorphic splitting (or isometric splitting in the particular class of Berwald spaces). By analogous techniques to the Riemannian case, I also exhibit the rigidity results of logarithmic Sobolev and Bakry-Ledoux isoperimetric inequalities via needle decomposition for reversible Finsler manifolds. This splitting phenomenon is comparable to the Cheeger-Gromoll type splitting theorem by Ohta.
Research Progress Status	令和3年度が最終年度であるため、記入しない。
Strategy for Future Research Activity	令和3年度が最終年度であるため、記入しない。