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arXiv · 2110.00292

A reverse H\"older inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces

Mustafa Alper Gunes·Andrea Mondino
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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-H\"older 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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Mustafa Alper Gunes, Andrea Mondino. 2021-10-01. A reverse H\"older inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces. https://doi.org/10.1090/proc%2F16099

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