Ricci curvature and monotonicity for harmonic functions
Name
Colding_Ricci curvature.pdf
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169.66 KB
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Adobe PDF
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e75a8e5ec043aeb5c9dd47b5da0d7981
Author(s)
Colding, Tobias
Minicozzi, William
Date Issued
February 2013
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
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00526-013-0610-z
