Ricci curvature and monotonicity for harmonic functions
Tobias Holck Colding, William P. Minicozzi II,
2012.09.20
http://arxiv.org/abs/1209.4669
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.
