A reverse H\"older inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces
Differential Geometry
2022-11-11 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2110.00292,
title = {A reverse H\"older inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces},
author = {Mustafa Alper Gunes and Andrea Mondino},
journal= {arXiv preprint arXiv:2110.00292},
year = {2022}
}
Comments
14 pages. Final Version, to appear in the Proc. Amer. Math. Soc