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

Gunes, Mustafa; Mondino, Andrea

doi:10.1090/proc/16099

A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on $\operatorname {RCD}(K,N)$ spaces
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by Mustafa Alper Gunes and Andrea Mondino

Proc. Amer. Math. Soc. 151 (2023), 295-311

DOI: https://doi.org/10.1090/proc/16099

Published electronically: September 23, 2022

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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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