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arXiv · 1810.02122

The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampere flows

Vincent Guedj·Hoang Chinh Lu·Ahmed Zeriahi
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Abstract

We develop the first steps of a parabolic pluripotential theory in bounded strongly pseudo-convex domains of Cn. We study certain degenerate parabolic complex Monge-Amp{\`e}re equations, modelled on the K{\"a}hler-Ricci flow evolving on complex algebraic varieties with Kawamata log-terminal singularities. Under natural assumptions on the Cauchy-Dirichlet boundary data, we show that the envelope of pluripotential subsolutions is semi-concave in time and continuous in space, and provides the unique pluripotential solution with such regularity.

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BibTeXRIS

Vincent Guedj, Hoang Chinh Lu, Ahmed Zeriahi. 2018-10-04. The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampere flows. https://arxiv.org/abs/1810.02122

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