Equality in the logarithmic Sobolev inequality

Shin ichi Ohta, Asuka Takatsu

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We investigate the rigidity problem for the logarithmic Sobolev inequality on weighted Riemannian manifolds satisfying Ric ≥ K> 0. 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.

Original languageEnglish
Pages (from-to)271-282
Number of pages12
Journalmanuscripta mathematica
Issue number1-2
Publication statusPublished - 2020 May 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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