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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-Ampère measures converges weakly. This criterion can be used to obtained a bounded \(\omega \) -plurisubharmonic solution to the Monge-Ampère equation.

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Weak Convergence of Monge-Ampère Measures on Compact Hermitian Manifolds

  • 会议论文

  • 发表日期：

    2025年

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  • Sławomir Kołodziej,
  • Ngoc Cuong Nguyen

摘要

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-Ampère measures converges weakly. This criterion can be used to obtained a bounded \(\omega \) -plurisubharmonic solution to the Monge-Ampère equation.