Ricci curvature and monotonicity for harmonic functions

Author(s)
Colding, Tobias; Minicozzi, William
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Abstract
In this paper we generalize the monotonicity formulas of “Colding (Acta Math 209:229–263, 2012)” for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., “Almgren (Preprint)”, “Colding and Minicozzi II (PNAS, 2012)”, “Garofalo and Lin (Indiana Univ Math 35:245–267, 1986)” 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.
Description
Original manuscript September 20, 2012
Date issued
2013-02
URI
http://hdl.handle.net/1721.1/79897
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Calculus of Variations and Partial Differential Equations
Publisher
Springer-Verlag
Citation
Colding, Tobias Holck, and William P. Minicozzi. “Ricci curvature and monotonicity for harmonic functions.” Calculus of Variations and Partial Differential Equations (February 26, 2013).
Version: Original manuscript
ISSN
0944-2669
1432-0835
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