Convergence of complete Ricci-βat manifolds
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2020
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| Online Access: | https://hdl.handle.net/1721.1/126935 |
| _version_ | 1826215184816930816 |
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| author | Park, Jiewon. |
| author2 | Tobias Holck Colding. |
| author_facet | Tobias Holck Colding. Park, Jiewon. |
| author_sort | Park, Jiewon. |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 |
| first_indexed | 2024-09-23T16:18:55Z |
| format | Thesis |
| id | mit-1721.1/126935 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:18:55Z |
| publishDate | 2020 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1269352020-09-04T03:02:43Z Convergence of complete Ricci-βat manifolds Park, Jiewon. Tobias Holck Colding. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 Cataloged from the official PDF of thesis. Includes bibliographical references (pages 57-59). This thesis is focused on the convergence at inαnity of complete Ricci βat manifolds. In the αrst part of this thesis, we will give a natural way to identify between two scales, potentially arbitrarily far apart, in the case when a tangent cone at inαnity has smooth cross section. The identiαcation map is given as the gradient βow of a solution to an elliptic equation. We use an estimate of Colding-Minicozzi of a functional that measures the distance to the tangent cone. In the second part of this thesis, we prove a matrix Harnack inequality for the Laplace equation on manifolds with suitable curvature and volume growth assumptions, which is a pointwise estimate for the integrand of the aforementioned functional. This result provides an elliptic analogue of matrix Harnack inequalities for the heat equation or geometric βows. by Jiewon Park. Ph. D. Ph.D. Massachusetts Institute of Technology, Department of Mathematics 2020-09-03T16:42:00Z 2020-09-03T16:42:00Z 2020 2020 Thesis https://hdl.handle.net/1721.1/126935 1191267704 eng MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided. http://dspace.mit.edu/handle/1721.1/7582 59 pages ; application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Park, Jiewon. Convergence of complete Ricci-βat manifolds |
| title | Convergence of complete Ricci-βat manifolds |
| title_full | Convergence of complete Ricci-βat manifolds |
| title_fullStr | Convergence of complete Ricci-βat manifolds |
| title_full_unstemmed | Convergence of complete Ricci-βat manifolds |
| title_short | Convergence of complete Ricci-βat manifolds |
| title_sort | convergence of complete ricci βat manifolds |
| topic | Mathematics. |
| url | https://hdl.handle.net/1721.1/126935 |
| work_keys_str_mv | AT parkjiewon convergenceofcompletericcibatmanifolds |