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Göteborgs universitets publikationer

A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics

Författare och institution:
Robert Berman (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Advances in Mathematics, 248 s. 1254-1297
ISSN:
0001-8708
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2013
Språk:
engelska
Fulltextlänk:
Sammanfattning (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 Miller manifolds are given. Tian's alpha-invariant is generalized to singular measures, allowing in particular a proof of the existence of Kahler-Einstein metrics with positive Ricci curvature that are singular along a given anti-canonical divisor (which combined with very recent developments concerning Miller metrics with conical singularities confirms a recent conjecture of Donaldson). As another application we show that if the Calabi flow in the (anti-)canonical class exists for all times then it converges to a Kahler-Einstein metric, when a unique one exists, which is in line with a well-known conjecture. (C) 2013 Elsevier Inc. All rights reserved.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
Monge-Ampere equation, Kahler-Einstein manifolds, Variational methods, SCALAR CURVATURE, HOLDER CONTINUITY, COMPLEX-SURFACES, K-ENERGY, MANIFOLDS, SPACE, CONVERGENCE, EXISTENCE, FLOW
Postens nummer:
186267
Posten skapad:
2013-11-08 11:30
Posten ändrad:
2016-07-01 11:38

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