Regularizing properties of the twisted K\"ahler-Ricci flow

TL;DR

This paper demonstrates that the twisted K"ahler-Ricci flow on a compact K"ahler manifold can start from any positive closed current with zero Lelong numbers and instantly smooth it, revealing regularizing properties.

Contribution

It establishes the immediate smoothing effect of the twisted K"ahler-Ricci flow starting from arbitrary positive closed currents with zero Lelong numbers.

Findings

Flow can be initiated from arbitrary positive closed currents.

Immediate smoothing of initial currents with zero Lelong numbers.

Enhances understanding of regularizing properties of the K"ahler-Ricci flow.

Abstract

Let $X$ be a compact K\"ahler manifold. We show that the K\"ahler-Ricci flow (as well as its twisted versions) can be run from an arbitrary positive closed current with zero Lelong numbers and immediately smoothes it.