Pluripotential Monge-Ampere flows in big cohomology classes

We study pluripotential complex Monge-Ampere flows in big cohomology classes on compact Kahler manifolds. We use the Perron method, considering pluripotential subsolutions to the Cauchy problem. We prove that, under natural assumptions on the data, the upper envelope of all subsolutions is continuous in space and semi-concave in time, and provides a unique pluripotential solution with such regularity. We apply this theory to study pluripotential Kahler-Ricci flows on compact Kahler manifolds of general type as well as on stable varieties (c) 2021 Elsevier Inc. All rights reserved.