Ricci curvature and monotonicity for harmonic functions
Differential Geometry
2012-09-24 v1 Analysis of PDEs
Abstract
In this paper we generalize the monotonicity formulas of [C] for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., [A], [CM1] and [GL] for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green's function on open manifolds with nonnegative Ricci curvature are asymptotically umbilic.
Keywords
Cite
@article{arxiv.1209.4669,
title = {Ricci curvature and monotonicity for harmonic functions},
author = {Tobias Holck Colding and William P. Minicozzi},
journal= {arXiv preprint arXiv:1209.4669},
year = {2012}
}