Elliptic PDEs on Compact Ricci Limit Spaces and Applications

Download or read book Elliptic PDEs on Compact Ricci Limit Spaces and Applications written by Shouhei Honda and published by . This book was released on 2018 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we study elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular we establish continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. We apply these to the study of second-order differential calculus on such limit spaces.