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 C1,1 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.
|Commitee:||Bedford, Eric, Lawson, Blaine, Varolin, Dror|
|School:||State University of New York at Stony Brook|
|School Location:||United States -- New York|
|Source:||DAI-B 75/12(E), Dissertation Abstracts International|
|Keywords:||Complex monge-ampere equations, Geodesics, Kahler-einstein metrics|
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