Handle crushing harmonic maps between surfaces
| dc.contributor.advisor | Wolf, Michael | en_US |
| dc.creator | Huang, Andy C | en_US |
| dc.date.accessioned | 2017-08-02T18:45:19Z | en_US |
| dc.date.available | 2017-08-02T18:45:19Z | en_US |
| dc.date.created | 2016-05 | en_US |
| dc.date.issued | 2016-04-20 | en_US |
| dc.date.submitted | May 2016 | en_US |
| dc.date.updated | 2017-08-02T18:45:19Z | en_US |
| dc.description.abstract | In this thesis, we construct polynomial growth harmonic maps from once-punctured Riemann surfaces of any finite genus to any even-sided, regular, ideal polygon in the hyperbolic plane. We also establish their uniqueness within a class of maps which differ by exponentially decaying variations. Previously, harmonic maps from C (which are conformally once-punctured spheres) to H^2 have been parameterized by holomorphic quadratic differentials on C. Our harmonic maps, mapping a genus g>1 punctured surface to a k-sided polygon, correspond to meromorphic quadratic differentials with one pole of order (k+2) at the puncture and (4g+k−2) zeros (counting multiplicity). In this way, we can associate to these maps a holomorphic quadratic differential on the punctured Riemann surface domain. As an example, we explore a special case of our theorems: the unique harmonic map from a punctured square torus to an ideal square. We use the symmetries of the map to deduce the three possibilities for its Hopf differential. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Huang, Andy C. "Handle crushing harmonic maps between surfaces." (2016) Diss., Rice University. <a href="https://hdl.handle.net/1911/96251">https://hdl.handle.net/1911/96251</a>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/96251 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | Harmonic maps | en_US |
| dc.subject | Differential geometry | en_US |
| dc.title | Handle crushing harmonic maps between surfaces | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Mathematics | en_US |
| thesis.degree.discipline | Natural Sciences | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
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