Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. / Includes bibliographical references (p. 80). / In this thesis, I study pseudo-holomorphic curves in symplectisation of the unit cotangent bundle of a Riemann surface of genus greater than 1. The contact form and compatible almost complex structure are both constructed from a metric on the Riemann surface whose curvature is constant -1. I related the pseudo-holomorphic curve equation to harmonic map equations and a Cauchy-Riemann type equation perturbed with quadratic terms for functions on a punctured Riemann sphere. Then I prove a Theorem that gives one to one correspondence between solutions to the perturbed Cauchy-Riemann equation and finite energy pseudo-holomorphic curves. / by Wei Luo. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/29984 |
| Date | January 2003 |
| Creators | Luo, Wei, 1975- |
| Contributors | Shing-Tung Yau., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 80 p., 2580726 bytes, 2580534 bytes, application/pdf, application/pdf, application/pdf |
| Rights | 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 |
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