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Conical Kahler-Einstein metrics and Its Applications

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dc.contributor.advisor Chen, Xiuxiong en_US
dc.contributor.author Yao, Chengjian en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2017-09-20T16:50:11Z
dc.date.available 2017-09-20T16:50:11Z
dc.date.issued 2015-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76414 en_US
dc.description 63 pgs en_US
dc.description.abstract In this dissertation we prove certain deformation behaviors of Kahler-Einstein metrics with singularities. Based on smooth approximation and a priori estimates, we first give a new proof to Donaldson's Openness Theorem of deforming the cone angle of conical Kahler-Einstein metric on smooth Fano manifold, and prove a direct generalization to conical Kahler-Einstein metrics along simple normal crossing pluri-anti-canonical divisors on smooth Fano manifold. Then we use continuity method to study the deformation of weak conical Kahler-Einstein metric on Q-Fano variety. The idea of our new proof above is generalized to prove the openness part of the continuity method argument, while the closedness part directly follows from the weak compactness result of Chen-Donaldson-Sun. en_US
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 en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.subject.other conical Kahler-Einstein metric, deforming cone angle, log-Mabuchi-functional, weak Kahler-Einstein metric en_US
dc.title Conical Kahler-Einstein metrics and Its Applications en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Lawson, Blaine en_US
dc.contributor.committeemember Bedford, Eric en_US
dc.contributor.committeemember Varolin, Dror en_US
dc.contributor.committeemember Rocek, Martin en_US

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