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The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampere flows (1810.02122v1)
Published 4 Oct 2018 in math.DG, math.AP, and math.CV
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.