Pluripotential kahler-ricci flows

TL;DR

This paper develops a new pluripotential theory for degenerate parabolic complex Monge-Ampère equations on compact Kähler manifolds, extending classical theory and applying it to Kähler-Ricci flows on singular varieties.

Contribution

It introduces a parabolic pluripotential framework and extends Bedford-Taylor theory to study weak solutions of Kähler-Ricci flows on singular varieties.

Findings

Established a parabolic pluripotential theory for degenerate equations

Extended Bedford-Taylor theory to the parabolic setting

Applied the theory to analyze Kähler-Ricci flows on log terminal singularities

Abstract

We develop a parabolic pluripotential theory on compact K{\"a}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{\`e}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{\"a}hler-Ricci flow on varieties with log terminal singularities.