{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Applications of the Seiberg-Witten equations to the Differential Geometry of non-compact Kahler manifolds","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76392"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"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."},{"label":"dcterms.available","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.contributor","value":"LeBrun, Claude R."},{"label":"dcterms.creator","value":"Elson, Ilya"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"81 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76392"},{"label":"dcterms.issued","value":"2014-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:09Z (GMT). No. of bitstreams: 1\nElson_grad.sunysb_0771E_12063.pdf: 517008 bytes, checksum: bd944a1696aa1f92df347a6bd0b9748b (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Differential Geometry, Gauge Theory, Kahler Geometry, Seiberg-Witten Equations"},{"label":"dcterms.title","value":"Applications of the Seiberg-Witten equations to the Differential Geometry of non-compact Kahler manifolds"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/62%2F85%2F10%2F62851019046516292635942490755313691117/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/62%2F85%2F10%2F62851019046516292635942490755313691117","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}