Type
Text
Type
Dissertation
Advisor
Chen, Xiuxiong | Lawson, Blaine | Bedford, Eric | Varolin, Dror | Rocek, Martin.
Date
2015-12-01
Keywords
Mathematics | conical Kahler-Einstein metric, deforming cone angle, log-Mabuchi-functional, weak Kahler-Einstein metric
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76414
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
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. | 63 pages
Recommended Citation
Yao, Chengjian, "Conical Kahler-Einstein metrics and Its Applications" (2015). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2337.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2337