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Cited by 9Geometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchNonlinear Partial Differential Equations

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Mean curvature flow from conical singularities

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Chodosh, Otis, Daniels-Holgate, J. M., Schulze, Felix·2024·Inventiones mathematicae
DOI 10.1007/s00222-024-01296-8
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Abstract

We prove Ilmanen’s resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface$M^{n}\subset \mathbb{R}^{n+1}$Mn⊂Rn+1,$2\leq n\leq 6$2≤n≤6, with an isolated conical singularity is modeled on the level set flow of the cone. In particular, the flow fattens (instantaneously) if and only if the level set flow of the cone fattens.

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References 43 · Cited by 9

Research works printed but not linked: 47

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Metadata

Authors
Chodosh, O., Daniels-Holgate, J. M., & Schulze, F.
Affiliations
  • Stanford University (US)
  • Hebrew University of Jerusalem (IL)
  • University of Warwick (GB)
Corresponding author
Schulze, Felix
ORCID
Venue
Inventiones mathematicae
Publisher
Springer Science and Business Media LLC
Published
2024-11-08
Volume
238
Issue
3
Pages
1041-1066
ISSN
  • 0020-9910 (ISSN-L)
  • 1432-1297
DOI
10.1007/s00222-024-01296-8
OpenAlex
W4404186054
Cited by
9
References
43
Citations by year
2026: 3 · 2025: 1 · 2024: 4
FWCI
2.56
Type
journal article
Language
en
Open access
Licence
Locations
  • Inventiones mathematicae (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • Warwick Research Archive Portal (University of Warwick) (submittedVersion, cc-by)
  • arXiv (Cornell University) (cc-by)
Funders
  • National Science Foundation (2304432)
  • University of Warwick
  • European Commission
Topics
  • Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
  • Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
  • Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Partial Differential Equations
Keywords
mean curvature flow, conical singularities, fattening, hypersurfaces

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CoChat. (2026). Citation check: Mean curvature flow from conical singularities. https://app.cochat.ai/papers/10.1007/s00222-024-01296-8
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Chodosh, O., Daniels-Holgate, J. M., & Schulze, F. (2024). Mean curvature flow from conical singularities. Inventiones mathematicae. https://doi.org/10.1007/s00222-024-01296-8