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arXiv · 1209.4669

Ricci curvature and monotonicity for harmonic functions

Tobias Holck Colding·William P. Minicozzi II
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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.

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Tobias Holck Colding, William P. Minicozzi II. 2012-09-20. Ricci curvature and monotonicity for harmonic functions. https://arxiv.org/abs/1209.4669

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