Applications of the Seiberg-Witten equations to the Differential Geometry of non-compact Kähler manifolds
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چکیده
of the Dissertation Applications of the Seiberg-Witten equations to the Differential Geometry of non-compact Kähler manifolds by Ilya Elson Doctor of Philosophy in Mathematics Stony Brook University 2014 Soon after the introduction of the Seiberg-Witten equations, and their magnificent application to the differential topology of 4manifolds, LeBrun [LeB95a] 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. Finally, Di Cerbo[DC12, DC11] applied Biquard’s techniques to Σ× Σg. The main tool that allows one to use the Seiberg-Witten equations to
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