Weak convergence of Monge-Amp\`ere measures on compact Hermitian manifolds

Slawomir Kolodziej; Ngoc Cuong Nguyen

Weak convergence of Monge-Amp\`ere measures on compact Hermitian manifolds

Complex Variables 2022-12-23 v1

Authors: Slawomir Kolodziej , Ngoc Cuong Nguyen

Abstract

We give a sufficient condition on a sequence of uniformly bounded $\omega$ -plurisubharmonic functions, $\omega$ being a Hermitian metric, for which the sequence of associated Monge-Amp\`ere measures converges weakly. This criterion can be used to obtained a bounded $\omega$ -plurisubharmonic solution to the Monge-Amp\`ere equation.

Keywords

monge-ampere measures weak convergence hermitian manifolds plurisubharmonic functions monge-ampere equation

Cite

@article{arxiv.2212.11550,
  title  = {Weak convergence of Monge-Amp\`ere measures on compact Hermitian manifolds},
  author = {Slawomir Kolodziej and Ngoc Cuong Nguyen},
  journal= {arXiv preprint arXiv:2212.11550},
  year   = {2022}
}

Comments

This is an expository paper, 9 pages

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