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How close is too close for singular mean curvature flows?
Open accessAbstract
Suppose $$(M^i_t)_{t\in [0,T)}$$ ( M t i ) t ∈ [ 0 , T ) , $$i=1,2$$ i = 1 , 2 , are two mean curvature flows in $$\mathbb {R}^{n+1}$$ R n + 1 encountering a multiplicity one compact singularity at time T , in such a manner that for every k , the Hausdorff distance between the two flows, $$d_H$$ d H , satisfies $$d_{H}(M^1_t,M^2_t)/(T-t)^k \rightarrow 0$$ d H ( M t 1 , M t 2 ) / ( T - t ) k → 0 . We demonstrate that $$M^1_t=M^2_t$$ M t 1 = M t 2 for every t . This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where $$M^1_t$$ M t 1 is itself a self-similarly shrinking flow.
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References 16 · Cited by 3
Research works printed but not linked: 16
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Metadata
- Authors
- Daniels-Holgate, J. M., & Hershkovits, O.
- Affiliations
- Queen Mary University of London (GB)
- Hebrew University of Jerusalem (IL)
- Corresponding author
- Daniels-Holgate, J. M.
- Venue
- Calculus of Variations and Partial Differential Equations
- Published
- 2026-07-18
- Volume
- 65
- Issue
- 8
- Pages
- 234-234
- ISSN
- 0944-2669 (ISSN-L)
- 1432-0835
- OpenAlex
- W4417285854
- Cited by
- 3
- References
- 16
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Calculus of Variations and Partial Differential Equations (publishedVersion, cc-by)
- PubMed (publishedVersion)
- PubMed Central (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- HORIZON EUROPE European Research Council (101116390)
- Engineering and Physical Sciences Research Council (EP/Y017862/1)
- 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, singularities, Hausdorff distance, singularity resolution
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