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Cited by 11Geometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchGeometric and Algebraic Topology

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Revisiting generic mean curvature flow in ℝ 3

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Chodosh, Otis, Choi, Kyeongsu, Mantoulidis, Christos, Schulze, Felix·2026·Journal für die reine und angewandte Mathematik (Crelles Journal)
DOI 10.1515/crelle-2025-0064
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Abstract

Bamler–Kleiner recently proved a multiplicity-one theorem for mean curvature flow in R 3 \mathbb{R}^{3} and combined it with the authors’ work on generic mean curvature flows to fully resolve Huisken’s genericity conjecture. In this paper, we show that a short density-drop theorem plus the Bamler–Kleiner multiplicity-one theorem for tangent flows at the first nongeneric singular time suffice to resolve Huisken’s conjecture – without relying on the strict genus-drop theorem for one-sided ancient flows previously established by the authors.

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References 38 · Cited by 11

Research works printed but not linked: 41

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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
Chodosh, Otis
ORCID
Venue
Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher
Walter de Gruyter GmbH
Published
2025-10-08
Volume
2026
Issue
835
Pages
219-232
ISSN
  • 0075-4102 (ISSN-L)
  • 1435-5345
DOI
10.1515/crelle-2025-0064
OpenAlex
W4414890838
Cited by
11
References
38
Citations by year
2026: 6 · 2025: 4
FWCI
6.31
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal für die reine und angewandte Mathematik (Crelles Journal) (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • Warwick Research Archive Portal (University of Warwick) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (DMS-2304432, DMS-2403728)
  • Korea Institute for Advanced Study (MG078902)
Topics
  • Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
  • Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
  • Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
Keywords
mean curvature flow, multiplicity one theorem, tangent flows, singularity formation, three-dimensional space

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CoChat. (2026). Citation check: Revisiting generic mean curvature flow in ℝ 3. https://app.cochat.ai/papers/10.1515/crelle-2025-0064
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Chodosh, O., Choi, K., Mantoulidis, C., & Schulze, F. (2026). Revisiting generic mean curvature flow in ℝ 3. Journal für die reine und angewandte Mathematik (Crelles Journal). https://doi.org/10.1515/crelle-2025-0064