论文标题
光谱差距的僵化结果及其应用
A rigidity result of spectral gap on Finsler manifolds and its application
论文作者
论文摘要
我们研究了加权RICCI曲率绑定$ \ text {ric} _ {\ infty} \ geq k> 0 $的Finsler歧管上尖锐的频谱差距的刚度问题。我们的主要结果表明，如果平等成立，则歧管必定会接受差异分裂（或在特定类别的Berwald空间中的等距分裂）。这种分裂现象与Ohta的Cheeger-Gromoll类型分裂定理相当。我们还通过针头分解作为推论，获得对数Sobolev和Bakry Ledoux等仪不平等的刚度结果。
We investigate the rigidity problem for the sharp spectral gap on Finsler manifolds of weighted Ricci curvature bound $\text{Ric}_{\infty} \geq K > 0$. 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.
