| dc.contributor.author | Colding, Tobias | |
| dc.contributor.author | Minicozzi, William | |
| dc.date.accessioned | 2013-02-28T16:56:09Z | |
| dc.date.available | 2013-02-28T16:56:09Z | |
| dc.date.issued | 2012-08 | |
| dc.date.submitted | 2012-06 | |
| dc.identifier.issn | 0027-8424 | |
| dc.identifier.issn | 1091-6490 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/77236 | |
| dc.description.abstract | In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicity for parabolic operators, we turn to their elliptic counterparts, their geometric meaning, and some geometric consequences. | 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 0906233) | 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.description.sponsorship | National Science Foundation (U.S.) (Grant 0932078) | en_US |
| dc.language.iso | en_US | |
| dc.publisher | National Academy of Sciences (U.S.) | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1073/pnas.1203856109 | en_US |
| dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
| dc.source | PNAS | en_US |
| dc.title | Monotonicity and its analytic and geometric implications | en_US |
| dc.type | Article | en_US |
| dc.identifier.citation | Colding, T. H., and W. P. Minicozzi. “Monotonicity and Its Analytic and Geometric Implications.” Proceedings of the National Academy of Sciences (2012). | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
| dc.contributor.mitauthor | Colding, Tobias | |
| dc.contributor.mitauthor | Minicozzi, William | |
| dc.relation.journal | Proceedings of the National Academy of Sciences of the United States of America | en_US |
| dc.eprint.version | Final published version | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dspace.orderedauthors | Colding, T. H.; Minicozzi, W. P. | en |
| dc.identifier.orcid | https://orcid.org/0000-0001-6208-384X | |
| dc.identifier.orcid | https://orcid.org/0000-0003-4211-6354 | |
| mit.license | PUBLISHER_CC | en_US |
| mit.metadata.status | Complete | |
