| dc.identifier.uri | http://hdl.handle.net/11401/76392 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | Soon after the introduction of the Seiberg-Witten equations, and their magnificent application to the differential topology of 4-manifolds, LeBrun [LeB95] used these equations to study differential geometry and prove a rigidity theorem for compact complex hyperbolic manifolds. Biquard [Biq97] extended these results to non-compact, finite volume complex hyperbolic manifolds, and Rollin [Rol04] extended these techniques to CH<sup>2</sup>. Finally, Di Cerbo[DC12b, DC11] applied Biquard's techniques to the product of two negatively curved Riemann surfaces. The main tool that allows one to use the Seiberg-Witten equations to study differential geometry is an integral scalar curvature estimate The principle difficulty in extending these methods to the non-compact case, which was overcome by Biquard, Rollin and Di Cerbo is the proof of the existence of a solution to the equations. Finally, in LeBrun used conformal rescaling of the Seiberg-Witten equations to prove an integral estimate that involves both the scalar and Weyl curvature. In this thesis we extend these techniques to quasiprojective 4-manifolds which admit negatively curved, finite volume Kahler-Einstein metrics. Following Biquard's method we produce an irreducible solution to the Seiberg-Witten equations on the non-compact manifold as a limit of solutions on the compactification, and then use the Weitzenbock formula to obtain a scalar curvature estimate that is necessary for geometric applications. | |
| dcterms.available | 2017-09-20T16:50:09Z | |
| dcterms.contributor | LeBrun, Claude R. | en_US |
| dcterms.contributor | Lawson, Blaine | en_US |
| dcterms.contributor | Anderson, Michael | en_US |
| dcterms.contributor | Rocek, Martin. | en_US |
| dcterms.creator | Elson, Ilya | |
| dcterms.dateAccepted | 2017-09-20T16:50:09Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:09Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 81 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76392 | |
| dcterms.issued | 2014-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:09Z (GMT). No. of bitstreams: 1
Elson_grad.sunysb_0771E_12063.pdf: 517008 bytes, checksum: bd944a1696aa1f92df347a6bd0b9748b (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Differential Geometry, Gauge Theory, Kahler Geometry, Seiberg-Witten Equations | |
| dcterms.subject | Mathematics | |
| dcterms.title | Applications of the Seiberg-Witten equations to the Differential Geometry of non-compact Kahler manifolds | |
| dcterms.type | Dissertation | |
