Singularity Types for Long-Time Chern-Ricci Flow

TL;DR

This paper extends results from Kähler-Ricci flow to Chern-Ricci flow, showing that under certain conditions, singularity types are independent of initial metrics within the same cohomology class.

Contribution

It demonstrates that solutions with bounded torsion and curvature lead to uniform bounds across all solutions starting from the same cohomology class.

Findings

Solutions with bounded torsion and curvature are stable across different initial metrics.

Singularity types are invariant for long-time solutions under specified conditions.

Uniform bounds on torsion and curvature imply consistent singularity behavior.

Abstract

We extend some results known for the K\"ahler-Ricci flow to the Chern-Ricci flow regarding the independence of singularity types for long-time solutions. Specifically, we show that if a solution to the Chern-Ricci flow exists with uniformly bounded torsion and curvature, then any other solution starting from an initial metric of the same $\partial \bar{\partial}$ class will also exhibit uniform bounds on torsion and curvature.