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Evolution of convex lens-shaped networks under the curve shortening flow
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Schnürer, Oliver C., Azouani, Abderrahim, Georgi, Marc, Hell, Juliette, Jangle, Nihar, Koeller, Amos, Marxen, Tobias, Ritthaler, Sandra, Sáez, Mariel, Schulze, Felix and Smith, Brian (2011) Evolution of convex lens-shaped networks under the curve shortening flow. Transactions of the American Mathematical Society, 363 (5). p. 2265. doi:10.1090/S0002-9947-2010-04820-2 ISSN 0002-9947.
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Official URL: http://dx.doi.org/10.1090/S0002-9947-2010-04820-2
Abstract
We consider convex symmetric lens-shaped networks in ℝ2 that evolve under the curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a self-similarly shrinking network, which we prove to be unique in an appropriate class. We also include a classification result for some self-similarly shrinking networks.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Transactions of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9947 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | 363 | ||||
Number: | 5 | ||||
Page Range: | p. 2265 | ||||
DOI: | 10.1090/S0002-9947-2010-04820-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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