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• W2950964022 abstract "We develop a variational calculus for a certain free energy functional on the space of all probability measures on a Kahler manifold X. This functional can be seen as a generalization of Mabuchi's K-energy functional and its twisted versions to more singular situations. Applications to Monge-Ampere equations of mean field type, twisted Kahler-Einstein metrics and Moser-Trudinger type inequalities on Kahler manifolds are given. Tian's alpha- invariant is generalized to singular measures, allowing i particular the construction of Kahler-Einstein metrics with positive Ricci curvature that are singular along a given anti-canonical divisor (as proposed in a very recent program of Donaldson). As another application we show that if the Calabi flow in the (anti-) canonical class exits for all times then it converges to a Kahler-Einstein metric, when one exists. Applications to the probabilistic/statistical mechanical approach to the construction of Kahler-Einstein metrics, very recently introduced by the author, will appear elsewhere." @default.
• W2950964022 created "2019-06-27" @default.
• W2950964022 creator A5073101289 @default.
• W2950964022 date "2010-11-17" @default.
• W2950964022 modified "2023-09-27" @default.
• W2950964022 title "A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics" @default.
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• W2950964022 hasPublicationYear "2010" @default.
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