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Cited by 64Geometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchNonlinear Partial Differential Equations

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Mean curvature flow with generic initial data

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Chodosh, Otis, Choi, Kyeongsu, Mantoulidis, Christos, Schulze, Felix·2024·Inventiones mathematicae
DOI 10.1007/s00222-024-01258-0
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Abstract

We show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$ R 3 avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in $\mathbb{R}^{4}$ R 4 is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons.

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Metadata

Authors
Chodosh, O., Choi, K., Mantoulidis, C., & Schulze, F.
Affiliations
  • Stanford University (US)
  • Korea Institute for Advanced Study (KR)
  • Rice University (US)
  • University of Warwick (GB)
Corresponding author
Schulze, Felix
ORCID
Venue
Inventiones mathematicae
Publisher
Springer Science and Business Media LLC
Published
2024-04-23
Volume
237
Issue
1
Pages
121-220
ISSN
  • 0020-9910 (ISSN-L)
  • 1432-1297
DOI
10.1007/s00222-024-01258-0
OpenAlex
W3027442782
Cited by
64
References
0
Citations by year
2026: 14 · 2025: 16 · 2024: 11
FWCI
13.10
Type
journal article
Language
en
Open access
Licence
Locations
  • Inventiones mathematicae (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • Warwick Research Archive Portal (University of Warwick) (submittedVersion, cc-by)
  • UCL Discovery (University College London) (submittedVersion)
  • Rice Research Repository (Rice University) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (2016403, 2304432, 1811059, 1905165)
  • Leverhulme Trust (RPG-2016-174, RPG-2016)
  • National Research Foundation
  • National Research Foundation of Korea (RS-2023-00219980)
  • Ministry of Science and ICT, South Korea (RS-2023-00219980, RS-2023)
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, shrinking solitons, singularity formation

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