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

@inproceedings{Gunes2021ARH, 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}, year={2021} }

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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