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In this article, we prove Talenti's comparison theorem for Poisson equationon complete noncompact Riemannian manifold with nonnegative Ricci curvature.Furthermore, we obtain the Faber-Krahn inequality for the first eigenvalue ofDirichlet Laplacian, $L^1$- and $L^\infty$-moment spectrum, especiallySaint-Venant theorem for torsional rigidity and a reverse H\"older inequalityfor eigenfunctions of Dirichlet Laplacian.

Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature