Monotonicity and its analytic and geometric implications
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 monotonicit...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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National Academy of Sciences (U.S.)
2013
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| Online Access: | http://hdl.handle.net/1721.1/77236 https://orcid.org/0000-0001-6208-384X https://orcid.org/0000-0003-4211-6354 |
| _version_ | 1826212921553715200 |
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| author | Colding, Tobias Minicozzi, William |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Colding, Tobias Minicozzi, William |
| author_sort | Colding, Tobias |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:40:17Z |
| format | Article |
| id | mit-1721.1/77236 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:40:17Z |
| publishDate | 2013 |
| publisher | National Academy of Sciences (U.S.) |
| record_format | dspace |
| spelling | mit-1721.1/772362022-10-02T03:18:26Z Monotonicity and its analytic and geometric implications Colding, Tobias Minicozzi, William Massachusetts Institute of Technology. Department of Mathematics Colding, Tobias Minicozzi, William 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. National Science Foundation (U.S.) (Grant DMS 11040934) National Science Foundation (U.S.) (Grant DMS 0906233) National Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774) National Science Foundation (U.S.). Focused Research Group (Grant DMS 0853501) National Science Foundation (U.S.) (Grant 0932078) 2013-02-28T16:56:09Z 2013-02-28T16:56:09Z 2012-08 2012-06 Article http://purl.org/eprint/type/JournalArticle 0027-8424 1091-6490 http://hdl.handle.net/1721.1/77236 Colding, T. H., and W. P. Minicozzi. “Monotonicity and Its Analytic and Geometric Implications.” Proceedings of the National Academy of Sciences (2012). https://orcid.org/0000-0001-6208-384X https://orcid.org/0000-0003-4211-6354 en_US http://dx.doi.org/10.1073/pnas.1203856109 Proceedings of the National Academy of Sciences of the United States of America 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. application/pdf National Academy of Sciences (U.S.) PNAS |
| spellingShingle | Colding, Tobias Minicozzi, William Monotonicity and its analytic and geometric implications |
| title | Monotonicity and its analytic and geometric implications |
| title_full | Monotonicity and its analytic and geometric implications |
| title_fullStr | Monotonicity and its analytic and geometric implications |
| title_full_unstemmed | Monotonicity and its analytic and geometric implications |
| title_short | Monotonicity and its analytic and geometric implications |
| title_sort | monotonicity and its analytic and geometric implications |
| url | http://hdl.handle.net/1721.1/77236 https://orcid.org/0000-0001-6208-384X https://orcid.org/0000-0003-4211-6354 |
| work_keys_str_mv | AT coldingtobias monotonicityanditsanalyticandgeometricimplications AT minicozziwilliam monotonicityanditsanalyticandgeometricimplications |