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

The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.

End-time regularity theorem for Brakke flows

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Stuvard, Salvatore, Tonegawa, Yoshihiro·2024·Mathematische Annalen
DOI 10.1007/s00208-024-02826-8
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Abstract

For a general k -dimensional Brakke flow in $${\mathbb {R}}^n$$ R n locally close to a k -dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smooth graph over the plane with estimates on all the derivatives up to the end-time. Moreover, at any point in space-time where the Gaussian density is close to 1, the flow can be extended smoothly as a mean curvature flow up to that time in a neighborhood: this extends White’s local regularity theorem to general Brakke flows. The regularity result is in fact obtained for more general Brakke-like flows, driven by the mean curvature plus an additional forcing term in a dimensionally sharp integrability class or in a Hölder class.

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Metadata

Authors
Stuvard, S., & Tonegawa, Y.
Affiliations
  • University of Milan (IT)
  • Tokyo Institute of Technology (JP)
Corresponding author
Stuvard, Salvatore
ORCID
Venue
Mathematische Annalen
Publisher
Springer Science and Business Media LLC
Published
2024-03-21
Volume
390
Issue
3
Pages
3317-3353
ISSN
  • 0025-5831 (ISSN-L)
  • 1432-1807
DOI
10.1007/s00208-024-02826-8
OpenAlex
W4393036215
Cited by
7
References
23
Citations by year
2026: 2 · 2025: 3 · 2024: 1
FWCI
1.92
Type
journal article
Language
en
Open access
Licence
Locations
  • Mathematische Annalen (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) (submittedVersion, cc-by)
  • Institutional Repositories DataBase (IRDB) (submittedVersion)
  • Tokyo Tech Research Repository (Tokyo Institute of Technology) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Ministero dell’Università e della Ricerca (PRIN 2022PJ9EFL)
  • Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
  • Japan Society for the Promotion of Science London (18H03670, 19H00639)
  • Università degli Studi di Milano
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
Brakke flow, mean curvature flow, singularities, Gaussian density, smooth extension, forcing term, Hölder regularity

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CoChat. (2026). Citation check: End-time regularity theorem for Brakke flows. https://app.cochat.ai/papers/10.1007/s00208-024-02826-8
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Stuvard, S., & Tonegawa, Y. (2024). End-time regularity theorem for Brakke flows. Mathematische Annalen. https://doi.org/10.1007/s00208-024-02826-8

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