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

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.