The K\"ahler-Ricci flow on pseudoconvex domains

TL;DR

This paper proves the existence and convergence of the Kähler-Ricci flow on pseudoconvex domains with general initial metrics, extending previous results to higher dimensions and removing curvature bounds.

Contribution

It establishes the existence, completeness, and convergence of the Kähler-Ricci flow on pseudoconvex domains without curvature restrictions, generalizing prior surface results.

Findings

Flow exists for general initial metrics

Flow is complete and converges to Kähler-Einstein metric

Generalizes Topping's surface results to higher dimensions

Abstract

We establish the existence of K\"ahler-Ricci flow on pseudoconvex domains with general initial metric without curvature bounds. Moreover we prove that this flow is simultaneously complete, and its normalized version converge to the complete K\"ahler-Einstein metric, which generalizes Topping's works on surfaces.