Accepted Paper

Inserted: 1 oct 2021
Last Updated: 4 apr 2022

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

Abstract:

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.

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• Gunes-Mondino-ReverseHolder-PAMS.pdf