Regularity of the Level Set Flow
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1606.05185.pdf
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155.62 KB
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Adobe PDF
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Author(s)
Colding, Tobias
Minicozzi, William
Date Issued
July 2017
Journal
Communications on Pure and Applied Mathematics
Publisher
Wiley-Blackwell
Citation
Colding, Tobias Holck, and William P. Minicozzi. “Regularity of the Level Set Flow.” Communications on Pure and Applied Mathematics, vol. 71, no. 4, Apr. 2018, pp. 814–24.
Version
Original manuscript
Abstract
We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative and satisfies the equation classically. We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed C[superscript 1] manifold with cylindrical singularities. © 2017 Wiley Periodicals, Inc.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/CPA.21703
