Calculus of Variations and Geometric Measure Theory

M. A. Gunes - A. Mondino

A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces

created by mondino on 01 Oct 2021
modified on 04 Apr 2022


Accepted Paper

Inserted: 1 oct 2021
Last Updated: 4 apr 2022

Journal: Proc. Amer. Math. Soc.
Year: 2021

ArXiv: 2110.00292 PDF


In the framework of (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by a positive constant in a synthetic sense, we establish a sharp and rigid reverse-Hölder inequality for first eigenfunctions of the Dirichlet Laplacian. This generalises to the positively curved and non-smooth setting the classical ``Chiti Comparison Theorem''. We also prove a related quantitative stability result which seems to be new even for smooth Riemannian manifolds.