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arXiv · 1905.00085

Regularity of elliptic and parabolic systems

Tobias Holck Colding·William P. Minicozzi II
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Abstract

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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Tobias Holck Colding, William P. Minicozzi II. 2019-04-30. Regularity of elliptic and parabolic systems. https://arxiv.org/abs/1905.00085

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