Pluripotential Monge-Ampère flows in big cohomology classes

Abstract

We study pluripotential complex Monge-Ampère flows in big cohomology classes on compact Kähler 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 Kähler-Ricci flows on compact Kähler manifolds of general type as well as on stable varieties