Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

N. De Ponti - A. Mondino - D. Semola

The equality case in Cheeger's and Buser's inequalities on $ \mathsf{RCD}$ spaces

created by mondino on 31 Aug 2020
modified by semola on 14 Apr 2021

[BibTeX]

Published Paper

Inserted: 31 aug 2020
Last Updated: 14 apr 2021

Journal: Journal of Functional Analysis
Volume: 281
Number: 3
Year: 2021
Doi: https://doi.org/10.1016/j.jfa.2021.109022

ArXiv: 2008.12358 PDF

Abstract:

We prove that the sharp Buser's inequality obtained in the framework of $\mathsf{RCD}(1,\infty)$ spaces by the first two authors is rigid, i.e. equality is obtained if and only if the space splits isomorphically a Gaussian. The result is new even in the smooth setting. We also show that the equality in Cheeger's inequality is never attained in the setting of $\mathsf{RCD}(K,\infty)$ spaces with finite diameter or positive curvature, and we provide several examples of spaces with Ricci curvature bounded below where these assumptions are not satisfied and the equality is attained.


Download:

Credits | Cookie policy | HTML 5 | CSS 2.1