The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampere flows
Differential Geometry
2018-10-05 v1 Analysis of PDEs
Complex Variables
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.
Cite
@article{arxiv.1810.02122,
title = {The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampere flows},
author = {Vincent Guedj and Hoang Chinh Lu and Ahmed Zeriahi},
journal= {arXiv preprint arXiv:1810.02122},
year = {2018}
}