The Kahler-Ricci flow through singularities

TL;DR

This paper establishes the existence, uniqueness, and continuation of the weak Kahler-Ricci flow on singular projective varieties, proposing an analytic approach to the Minimal Model Program with Ricci flow.

Contribution

It introduces a weak Kahler-Ricci flow framework on singular varieties and demonstrates its extension through birational transformations, linking Ricci flow with the Minimal Model Program.

Findings

Existence and uniqueness of weak Kahler-Ricci flow on log terminal singularities.

Continuation of the flow through divisorial contractions and flips.

Proposed an analytic version of the Minimal Model Program.

Abstract

We prove the existence and uniqueness of the weak Kahler-Ricci flow on projective varieties with log terminal singularities. It is also shown that the weak Kahler-Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. We then propose an analytic version of the Minimal Model Program with Ricci flow.