{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/29984"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/29984","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"On contact homology of the unit cotangent bundle of a Riemann surface with genus greater than one","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Luo, Wei, 1975-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Shing-Tung Yau."],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-22T22:21:42Z","subjects":["Mathematics."],"languages":["eng"],"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. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On contact homology of the unit cotangent bundle of a Riemann surface with genus greater than one"]}]}],"canonical_facts":{"dc:contributor.advisor":["Shing-Tung Yau."],"dc:contributor.department":["Massachusetts Institute of Technology. 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