The level-set flow of the topologist’s sine curve is smooth
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12220_2017_9868_ReferencePDF.pdf
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Author(s)
Lam, Casey
Lauer, Joseph
Date Issued
December 2018
Publisher
Springer US
Version
Author's final manuscript
Abstract
In this note we prove that the level-set flow of the topologist’s sine curve is a smooth closed curve. In Lauer (Geom Funct Anal 23(6): 1934–1961, 2013) it was shown by the second author that under the level-set flow, a locally connected set in the plane evolves to be smooth, either as a curve or as a positive area region bounded by smooth curves. Here we give the first example of a domain whose boundary is not locally connected for which the level-set flow is instantaneously smooth. Our methods also produce an example of a nonpath-connected set that instantly evolves into a smooth closed curve.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s12220-017-9868-2
