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Sökning: LAR1:gu > Tidskriftsartikel > Chalmers tekniska högskola > Berman Robert 1976 > Boucksom Sebastien

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  • Berman, Robert, 1976-, et al. (författare)
  • A variational approach to complex Monge-Ampere equations
  • 2013
  • Ingår i: Publications mathématiques. - 0073-8301. ; 117:1, s. 179-245
  • Tidskriftsartikel (refereegranskat)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.
  • Berman, Robert, 1976-, et al. (författare)
  • Fekete points and convergence towards equilibrium measures on complex manifolds
  • 2011
  • Ingår i: Acta Mathematica. - 1871-2509. ; 207:1, s. 1-27
  • Tidskriftsartikel (övrigt vetenskapligt)abstract
    • Building on the first two authors' previous results, we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth properties of balls of holomorphic sections, or equivalently as an asymptotic minimization of generalized Donaldson L-functionals. Our result yields in particular the proof of a well-known conjecture in pluripotential theory concerning the equidistribution of Fekete points, and it also gives the convergence of Bergman measures towards equilibrium for Bernstein-Markov measures. Applications to interpolation of holomorphic sections are also discussed.
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