Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers

TL;DR

This paper demonstrates that for any asymptotically conical shrinking gradient Ricci soliton, a Ricci flow on a closed manifold can develop a finite-time singularity modeled on it, without symmetry or Kähler assumptions.

Contribution

It establishes the existence of Ricci flows with singularities modeled on general asymptotically conical shrinkers, providing detailed asymptotic descriptions without symmetry constraints.

Findings

Finite-time singularities can be modeled on asymptotically conical shrinkers.

No symmetry or Kähler assumptions are necessary for the model.

Provides a precise asymptotic description of singularity formation.

Abstract

Given an asymptotically conical, shrinking, gradient Ricci soliton, we show that there exists a Ricci flow solution on a closed manifold that forms a finite-time singularity modeled on the given soliton. No symmetry or Kahler assumptions on the soliton are required. The proof provides a precise asymptotic description of the singularity formation.