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Pré-Publication, Document De Travail Année : 2018

THE PLURIPOTENTIAL CAUCHY-DIRICHLET PROBLEM FOR COMPLEX MONGE-AMPERE FLOWS

Résumé

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-Ampère equations, modelled on the Kähler-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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Dates et versions

hal-01887229 , version 1 (03-10-2018)
hal-01887229 , version 2 (19-07-2021)

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Citer

Vincent Guedj, Chinh H. Lu, Ahmed Zeriahi. THE PLURIPOTENTIAL CAUCHY-DIRICHLET PROBLEM FOR COMPLEX MONGE-AMPERE FLOWS. 2018. ⟨hal-01887229v1⟩
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