Closed Ricci flows with singularities modeled on asymptotically conical shrinkers

Stolarski, Maxwell

doi:10.2140/gt.2026.30.1277

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Closed Ricci flows with singularities modeled on asymptotically conical shrinkers

Maxwell Stolarski

Geometry & Topology 30 (2026) 1277–1370

DOI: 10.2140/gt.2026.30.1277

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 Kähler assumptions on the soliton are required. The proof provides a precise asymptotic description of the singularity formation.

Keywords

Ricci flow, singularity, Ricci soliton, asymptotically conical

Mathematical Subject Classification

Primary: 53E20

References

Publication

Received: 28 June 2022

Revised: 16 September 2025

Accepted: 20 October 2025

Published: 9 July 2026

Proposed: John Lott

Seconded: Tobias H Colding, Nataša Šešum

Authors

Maxwell Stolarski
Warwick Mathematics Institute University of Warwick Coventry United Kingdom
https://warwick.ac.uk/fac/sci/maths/people/staff/stolarski/

Open Access made possible by participating institutions via Subscribe to Open.

Volume 30, issue 4 (2026)