Ricci curvature and convergence of Lipschitz functions
Differential Geometry
2010-05-07 v1 Metric Geometry
Abstract
We give a definition of convergence of differential of Lipschitz functions with respect to measured Gromov-Hausdorff topology. As their applications, we give a characterization of harmonic functions with polynomial growth on asymptotic cones of manifolds with nonnegative Ricci curvature and Euclidean volume growth, and distributional Laplacian comparison theorem on limit spaces of Riemannian manifolds.
Keywords
Cite
@article{arxiv.1005.1040,
title = {Ricci curvature and convergence of Lipschitz functions},
author = {Shouhei Honda},
journal= {arXiv preprint arXiv:1005.1040},
year = {2010}
}
Comments
151 pages.