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Uniqueness of asymptotically conical tangent flows
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Chodosh, O. and Schulze, Felix (2021) Uniqueness of asymptotically conical tangent flows. Duke Mathematical Journal, 170 (16). pp. 3601-3657. doi:10.1215/00127094-2020-0098 ISSN 0012-7094.
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WRAP-Uniqueness-asymptotically-conical-tangent-flows-Shultz-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1072Kb) | Preview |
Official URL: https://doi.org/10.1215/00127094-2020-0098
Abstract
Singularities of the mean curvature flow of an embedded surface in R3
are expected to be modeled on self-shrinkers that are compact, cylindrical, or asymptotically conical. In order to understand the flow before and after the singular time, it is crucial to know the uniqueness of tangent flows at the singularity.
In all dimensions, assuming that the singularity is of multiplicity 1, uniqueness in the compact case has been established by the second-named author, and in the cylindrical case by Colding and Minicozzi. We show here the uniqueness of multiplicity-1 asymptotically conical tangent flows for mean curvature flow of hypersurfaces.
In particular, this implies that when a mean curvature flow has a multiplicity-1 conical singularity model, the evolving surface at the singular time has an (isolated) regular conical singularity at the singular point. This should lead to a complete understanding of how to “flow through” such a singularity.
Item Type: | Journal Article | ||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Flows (Differentiable dynamical systems), Singularities (Mathematics), Curves, Surfaces | ||||||||||||||||||
Journal or Publication Title: | Duke Mathematical Journal | ||||||||||||||||||
Publisher: | Duke University Press | ||||||||||||||||||
ISSN: | 0012-7094 | ||||||||||||||||||
Official Date: | 1 November 2021 | ||||||||||||||||||
Dates: |
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Volume: | 170 | ||||||||||||||||||
Number: | 16 | ||||||||||||||||||
Page Range: | pp. 3601-3657 | ||||||||||||||||||
DOI: | 10.1215/00127094-2020-0098 | ||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
Copyright Holders: | Copyright © 2021 Duke University Press | ||||||||||||||||||
Date of first compliant deposit: | 17 December 2020 | ||||||||||||||||||
Date of first compliant Open Access: | 7 December 2021 | ||||||||||||||||||
RIOXX Funder/Project Grant: |
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