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Peer-reviewedCC BYGeometry & Topology

Closed Ricci flows with singularities modeled on asymptotically conical shrinkers

  • Maxwell Stolarski1
  1. 1Warwick Mathematics Institute, University of Warwick, Coventry, United Kingdom
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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.1. Introduction 1277 2. Preliminaries on shrinking solitons 1280 3. Strategy of the proof of Theorem 1.1 1292 4. Setup 1294 5. Preliminary estimates 1307 6. Preservation and improvement of C 2 bounds 1312 7. Behavior of L 2 f .M / quantities 1333 8. Proof of Theorem 1.1 1336 Appendix A. Rounding out cones 1350 Appendix B. Harmonic map heat flow 1358 Appendix C. Hölder estimates in Euclidean space 1364 Appendix D.

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Cite

BibTeXRIS
BibTeX
@article{stolarski2026closed,
  title = {{Closed Ricci flows with singularities modeled on asymptotically conical shrinkers}},
  author = {Maxwell Stolarski},
  journal = {Geometry \& Topology},
  year = {2026},
  month = jul,
  doi = {10.2140/gt.2026.30.1277},
  url = {https://doi.org/10.2140/gt.2026.30.1277},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Closed Ricci flows with singularities modeled on asymptotically conical shrinkers
AU  - Maxwell Stolarski
PY  - 2026
DA  - 2026/07/09
JO  - Geometry & Topology
DO  - 10.2140/gt.2026.30.1277
UR  - https://doi.org/10.2140/gt.2026.30.1277
AB  - 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.1. Introduction 1277 2. Preliminaries on shrinking solitons 1280 3. Strategy of the proof of Theorem 1.1 1292 4. Setup 1294 5. Preliminary estimates 1307 6. Preservation and improvement of C 2 bounds 1312 7. Behavior of L 2 f .M / quantities 1333 8. Proof of Theorem 1.1 1336 Appendix A. Rounding out cones 1350 Appendix B. Harmonic map heat flow 1358 Appendix C. Hölder estimates in Euclidean space 1364 Appendix D.
SN  - 1364-0380
SN  - 1465-3060
ER  -