| dc.contributor.author | Colding, Tobias | |
| dc.contributor.author | Minicozzi, William | |
| dc.date.accessioned | 2013-08-21T17:25:22Z | |
| dc.date.available | 2013-08-21T17:25:22Z | |
| dc.date.issued | 2013-02 | |
| dc.date.submitted | 2012-09 | |
| dc.identifier.issn | 0944-2669 | |
| dc.identifier.issn | 1432-0835 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/79897 | |
| dc.description | Original manuscript September 20, 2012 | en_US |
| dc.description.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. | en_US |
| dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS 11040934) | en_US |
| dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS 1206827) | en_US |
| dc.description.sponsorship | National Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774) | en_US |
| dc.description.sponsorship | National Science Foundation (U.S.). Focused Research Group (Grant DMS 0853501) | en_US |
| dc.language.iso | en_US | |
| dc.publisher | Springer-Verlag | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1007/s00526-013-0610-z | en_US |
| dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
| dc.source | arXiv | en_US |
| dc.title | Ricci curvature and monotonicity for harmonic functions | en_US |
| dc.type | Article | en_US |
| dc.identifier.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). | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
| dc.contributor.mitauthor | Colding, Tobias | en_US |
| dc.contributor.mitauthor | Minicozzi, William | en_US |
| dc.relation.journal | Calculus of Variations and Partial Differential Equations | en_US |
| dc.eprint.version | Original manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/NonPeerReviewed | en_US |
| dspace.orderedauthors | Colding, Tobias Holck; Minicozzi, William P. | en_US |
| dc.identifier.orcid | https://orcid.org/0000-0001-6208-384X | |
| dc.identifier.orcid | https://orcid.org/0000-0003-4211-6354 | |
| mit.license | OPEN_ACCESS_POLICY | en_US |
| mit.metadata.status | Complete | |
