Area-contracting maps between rectangles
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2006
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| Online Access: | http://hdl.handle.net/1721.1/31158 |
| _version_ | 1811092064676347904 |
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| author | Guth, Lawrence |
| author2 | Tomasz S. Mrowka. |
| author_facet | Tomasz S. Mrowka. Guth, Lawrence |
| author_sort | Guth, Lawrence |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. |
| first_indexed | 2024-09-23T15:12:25Z |
| format | Thesis |
| id | mit-1721.1/31158 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T15:12:25Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/311582019-04-11T04:03:01Z Area-contracting maps between rectangles Guth, Lawrence Tomasz S. Mrowka. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. Includes bibliographical references (p. 207-208). In this thesis, I worked on estimating the smallest k-dilation of all diffeomorphisms between two n-dimensional rectangles R and S. I proved that for many rectangles there are highly non-linear diffeomorphisms with much smaller k-dilation than any linear diffeomorphism. When k is equal to n-l, I determined the smallest k-dilation up to a constant factor. For all values of k and n, I solved the following related problem up to a constant factor. Given n-dimensional rectangles R and S, decide if there is an embedding of S into R which maps each k-dimensional submanifold of S to an image with larger k-volume. I also applied the k-dilation techniques to two purely topological problems: estimating the Hopf invariant of a map from a 3-manifold to a high-genus surface, and determining whether there is a map of non-zero degree from a 3-manifold to a hyperbolic 3-manifold. by Lawrence Guth. Ph.D. 2006-02-02T18:53:55Z 2006-02-02T18:53:55Z 2005 2005 Thesis http://hdl.handle.net/1721.1/31158 61207020 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 208 p. 12338876 bytes 12365750 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Guth, Lawrence Area-contracting maps between rectangles |
| title | Area-contracting maps between rectangles |
| title_full | Area-contracting maps between rectangles |
| title_fullStr | Area-contracting maps between rectangles |
| title_full_unstemmed | Area-contracting maps between rectangles |
| title_short | Area-contracting maps between rectangles |
| title_sort | area contracting maps between rectangles |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/31158 |
| work_keys_str_mv | AT guthlawrence areacontractingmapsbetweenrectangles |