K\"ahler-Ricci Flow with Degenerate Initial Class

TL;DR

This paper extends the weak K"ahler-Ricci flow framework to initial classes that are not necessarily K"ahler, broadening the applicability of the flow in complex geometry.

Contribution

It develops a new setup for the weak K"ahler-Ricci flow starting from degenerate initial classes that are not K"ahler.

Findings

Established existence of weak flow from degenerate initial classes

Extended previous results to more general initial conditions

Provided new techniques for analyzing non-K"ahler initial classes

Abstract

In an earlier work joint with X. X. Chen and G. Tian, we introduced the weak K\"ahler-Ricci flow for various geometric motivations. In the current work, we take further consideration on setting up the weak flow. Namely, the initial class is allowed to be no longer K\"ahler.