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

Daguang Chen; Haizhong Li

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arXiv · 2104.05568

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

Daguang Chen·Haizhong Li

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Abstract

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

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Daguang Chen, Haizhong Li. 2021-04-12. Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature. https://arxiv.org/abs/2104.05568

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