Elliptic PDEs on compact Ricci limit spaces and applications
Differential Geometry
2015-12-15 v5 Analysis of PDEs
Metric Geometry
Abstract
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 Schrodinger 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.
Cite
@article{arxiv.1410.3296,
title = {Elliptic PDEs on compact Ricci limit spaces and applications},
author = {Shouhei Honda},
journal= {arXiv preprint arXiv:1410.3296},
year = {2015}
}
Comments
91 pages. Final version. To appear in Memoirs of the AMS