Talenti’s comparison theorem on Finsler manifolds with nonnegative Ricci curvature

We establish a Talenti-type comparison theorem for the Dirichlet problem associated with Poisson’s equation on complete noncompact Finsler manifolds having nonnegative Ricci curvature and Euclidean volume growth. The proof relies on anisotropic symmetrization arguments and leverages the sharp isoperimetric inequality recently established by Manini [Preprint, arXiv:2212.05130, 2022 ]. In addition, we characterize the rigidity of the comparison principle under the additional assumption that the reversibility constant of the Finsler manifold is finite. As application, we prove a Faber-Krahn inequality for the first Dirichlet eigenvalue of the Finsler-Laplacian.