The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Amp\`ere flow with a general measure on the right-hand side

Bowoo Kang

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arXiv · 2501.16765

The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Amp\`ere flow with a general measure on the right-hand side

Bowoo Kang

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Abstract

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

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Bowoo Kang. 2025-01-28. The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Amp\`ere flow with a general measure on the right-hand side. https://arxiv.org/abs/2501.16765

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