Growth of Balls of Holomorphic Sections and Energy at Equilibrium

@inproceedings{BOUCKSOM2008GrowthOB,
  title={Growth of Balls of Holomorphic Sections and Energy at Equilibrium},
  author={S{\'E}BASTIEN BOUCKSOM},
  year={2008}
}
  • SÉBASTIEN BOUCKSOM
  • Published 2008
Let L be a big line bundle on a compact complex manifold X. Given a non-pluripolar compact subset K of X and the weight φ of a continuous Hermitian metric e on L, we define the energy at equilibrium of (K, φ) as the Aubin-Mabuchi energy of the extremal psh weight associated to (K, φ). We prove the differentiability of the energy at equilibrium with respect to φ, and we show that this energy describes the asymptotic behaviour as k → ∞ of the volume of the sup-norm unit ball induced by (K, kφ) on… CONTINUE READING