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A variational approach to complex Monge-Ampere equations

Robert Berman (Institutionen för matematiska vetenskaper, matematik) ; Sebastien Boucksom ; Viincent Guedj ; Ahmed Zeriahi
Publications mathématiques (0073-8301). Vol. 117 (2013), 1, p. 179-245.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2010-02-19. Senast ändrad 2016-07-01.
CPL Pubid: 113220

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur