Equality in the logarithmic Sobolev inequality
Equality in the logarithmic Sobolev inequality
复制标题
对数 Sobolev 不等式中的等式
DOI：
10.1007/s00229-019-01134-9
复制
发表时间：
2019
期刊：
影响因子：
0.6
通讯作者：
Asuka Takatsu
中科院分区：
文献类型：
--
作者：
Shin-ichi Ohta;Asuka Takatsu
研究了加权黎曼流形上对数Sobolev不等式的刚性问题，满足。假设等式成立，我们证明了1维高斯空间必然是分裂的，类似于Cheng-Zhou关于谱隙的刚性结果以及Morgan关于等周不等式的刚性结果。证明的关键成分是由Klartag在黎曼流形上引入的针分解方法。我们还提出了几个相关的开放问题。
We investigate the rigidity problem for the logarithmic Sobolev inequality on weighted Riemannian manifolds satisfying. Assuming that equality holds, we show that the 1-dimensional Gaussian space is necessarily split off, similarly to the rigidity results of Cheng–Zhou on the spectral gap as well as Morgan on the isoperimetric inequality. The key ingredient of the proof is the needle decomposition method introduced on Riemannian manifolds by Klartag. We also present several related open problems.