The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Ampère flow with a general measure on the right-hand side

2025/01/28 by Kang, Bowoo · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.16765

Abstract

We show that the pluripotential Cauchy-Dirichlet problem for the complex Monge-Ampère flow is solvable for the right-hand side of the form dt \wedge dμ where dμ is dominated by a Monge-Ampère measure of a bounded plurisubharmonic function. In particular, we remove the strict positivity assumption on dμ. We use this result to prove the parabolic version of the bounded subsolution theorem due to Kolodziej in pluripotential theory.

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