Rigidity for the spectral gap on Rcd(K, ∞)-spaces

DOI10.1353/ajm.2020.0039zbMath1462.58014arXiv1709.04017OpenAlexW3083683866MaRDI QIDQ5147260

Shin-Ichi Ohta, Kazumasa Kuwada, Nicola Gigli, Christian Ketterer

Publication date: 3 February 2021

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.04017

zbMATH Keywords

spectral gapLaplacianmetric measure spacerigidity theoremRiemannian curvature-dimension condition

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Rigidity results (53C24)

Related Items (12)

Stability of eigenvalues and observable diameter in RCD\((1, \infty)\) spaces ⋮ Sharp Cheeger-buser type inequalities in \(\mathsf{RCD}(K,\infty)\) spaces ⋮ Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds ⋮ Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments ⋮ The rigidity of sharp spectral gap in non-negatively curved spaces ⋮ Extremal of log-Sobolev functionals and Li-Yau estimate on \(\mathrm{RCD}^* (K,N)\) spaces ⋮ On Gaussian interpolation inequalities ⋮ Rigidity for the isoperimetric inequality of negative effective dimension on weighted Riemannian manifolds ⋮ The equality case in Cheeger's and Buser's inequalities on \(\mathsf{RCD}\) spaces ⋮ Equality in the logarithmic Sobolev inequality ⋮ Quantitative estimates for the Bakry-Ledoux isoperimetric inequality ⋮ ON RIEMANNIAN MANIFOLDS WITH POSITIVE WEIGHTED RICCI CURVATURE OF NEGATIVE EFFECTIVE DIMENSION

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