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Göteborgs universitets publikationer

A variational approach to complex Monge-Ampere equations

Författare och institution:
Robert Berman (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Sebastien Boucksom (-); Viincent Guedj (-); Ahmed Zeriahi (-)
Publicerad i:
Publications mathématiques, 117 ( 1 ) s. 179-245
ISSN:
0073-8301
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2013
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
We show that degenerate complex Monge-Ampère equations in a big cohomology class of a compact Kähler manifold can be solved using a variational method, without relying on Yau’s theorem. Our formulation yields in particular a natural pluricomplex analogue of the classical logarithmic energy of a measure. We also investigate Kähler-Einstein equations on Fano manifolds. Using continuous geodesics in the closure of the space of Kähler metrics and Berndtsson’s positivity of direct images, we extend Ding-Tian’s variational characterization and Bando-Mabuchi’s uniqueness result to singular Kähler-Einstein metrics. Finally, using our variational characterization we prove the existence, uniqueness and convergence as k→∞ of k-balanced metrics in the sense of Donaldson both in the (anti)canonical case and with respect to a measure of finite pluricomplex energy.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
113220
Posten skapad:
2010-02-19 13:39
Posten ändrad:
2016-07-01 11:36

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