Degenerate Monge-Ampere equations over projective manifolds
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
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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/1721.1/34685 |
| _version_ | 1826209858182971392 |
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| author | Zhang, Zhou, Ph. D. Massachusetts Institute of Technology |
| author2 | Gang Tian. |
| author_facet | Gang Tian. Zhang, Zhou, Ph. D. Massachusetts Institute of Technology |
| author_sort | Zhang, Zhou, Ph. D. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. |
| first_indexed | 2024-09-23T14:33:02Z |
| format | Thesis |
| id | mit-1721.1/34685 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:33:02Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/346852019-04-12T09:19:04Z Degenerate Monge-Ampere equations over projective manifolds Zhang, Zhou, Ph. D. Massachusetts Institute of Technology Gang Tian. 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, 2006. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 253-257). In this thesis, we study degenerate Monge-Ampere equations over projective manifolds. The main degeneration is on the cohomology class which is Kähler in classic cases. Our main results concern the case when this class is semi-ample and big with certain generalization to more general cases. Two kinds of arguments are applied to study this problem. One is maximum principle type of argument. The other one makes use of pluripotential theory. So this article mainly consists of three parts. In the first two parts, we apply these two kinds of arguments separately and get some results. In the last part, we try to combine the results and arguments to achieve better understanding about interesting geometric objects. Some interesting problems are also mentioned in the last part for future consideration. The generalization of classic pluripotential theory in the second part may be of some interest by itself. by Zhou Zhang. Ph.D. 2006-11-07T17:26:57Z 2006-11-07T17:26:57Z 2006 2006 Thesis http://hdl.handle.net/1721.1/34685 71316778 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 257 p. 1166098 bytes 1160081 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Zhang, Zhou, Ph. D. Massachusetts Institute of Technology Degenerate Monge-Ampere equations over projective manifolds |
| title | Degenerate Monge-Ampere equations over projective manifolds |
| title_full | Degenerate Monge-Ampere equations over projective manifolds |
| title_fullStr | Degenerate Monge-Ampere equations over projective manifolds |
| title_full_unstemmed | Degenerate Monge-Ampere equations over projective manifolds |
| title_short | Degenerate Monge-Ampere equations over projective manifolds |
| title_sort | degenerate monge ampere equations over projective manifolds |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/34685 |
| work_keys_str_mv | AT zhangzhouphdmassachusettsinstituteoftechnology degeneratemongeampereequationsoverprojectivemanifolds |