On the weak K\"ahler-Ricci flow

TL;DR

This paper introduces a framework for analyzing the Kähler-Ricci flow starting from non-smooth initial data, expanding the applicability of the flow in complex geometry.

Contribution

It defines and studies the Kähler-Ricci flow with non-smooth initial conditions, providing new insights and potential applications in complex differential geometry.

Findings

Established existence of the flow from non-smooth data

Identified key properties and behaviors of the flow in this setting

Suggested applications to complex geometric problems

Abstract

In this note, we define and study K\"ahler-Ricci flow with initial data not being smooth with some natural applications.