Type
Text
Type
Dissertation
Advisor
Chen, Xiuxiong | Lawson, Blaine | Varolin, Dror | Bedford, Eric.
Date
2014-12-01
Keywords
Mathematics | complex Monge-Ampere equations, geodesics, Kaehler-Einstein metrics
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/11401/76401
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Bando and Mabuchi proved the uniqueness of Kaehler-Einstein metrics on Fano manifolds up to a holomorphic automorphism in 1987. Then recently Berndtsson generalized the uniqueness result of Kaehler-Einstein metrics to bounded potentials. We give a new proof of the Bando-Mabuch-Berndtsson uniqueness theorem in a different aspect, based on a new technique developed from Chen's C^{1,1} geodesic and Futaki's spectral formula. Finally, the uniqueness of the conical Kaehler-Einstein metrics will be discussed under the assumption of properness of twisted Ding-functional. | 61 pages
Recommended Citation
Li, Long, "On the Uniqueness of singular Kaehler-Einstein metrics" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2324.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2324