Elliptic PDEs on Compact Ricci Limit Spaces and Applications

Examines elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrodinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian.