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Regularity of elliptic and parabolic systems

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arxiv 1905.00085 v3 pith:XQECAWMD submitted 2019-04-30 math.DG math.AP

Tobias Holck Colding , William P. Minicozzi II This is my paper · ORCID
classification math.DGmath.AP
keywords codimensioncylindricalblowupscurvatureflowmeanparabolicregularity
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We show uniqueness of cylindrical blowups for mean curvature flow in all dimension and all codimension. Cylindrical singularities are known to be the most important; they are the most prevalent in any codimension. Mean curvature flow in higher codimension is a nonlinear parabolic system where many of the methods used for hypersurfaces do not apply and uniqueness of cylindrical blowups remained a major open problem. Our results imply regularity of the singular set for the system.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\infty$

    math.DG 2019-09 conditional novelty 7.0 of 10

    Ancient mean curvature flows that converge rapidly to a compact self-shrinker at time minus infinity must have the same codimension as the shrinker, and if the convergence is super-exponential the flow equals the shrinker.

  2. Construction of High Codimension Ancient Mean Curvature Flows

    math.DG 2019-08 conditional novelty 2.0 of 10

    The paper constructs high-codimension ancient curve shortening flows, but the abstract and Remark 1.3 state the construction was earlier discovered in AAAW13.

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