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  Evolution of convex lens-shaped networks under curve shortening flow

Schnürer, O. C., Azouani, A., Georgi, M., Hell, J., Jangle, N., Koeller, A., et al. (2011). Evolution of convex lens-shaped networks under curve shortening flow. Transactions of the American Mathematical Society, 363(5), 2265-2294. Retrieved from http://arxiv.org/abs/0711.1108.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-093A-4 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-093C-F
Genre: Journal Article

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 Creators:
Schnürer, Oliver C., Author
Azouani, Abderrahim, Author
Georgi, Marc, Author
Hell, Juliette, Author
Jangle, Nihar, Author
Koeller, Amos, Author
Marxen, Tobias, Author
Ritthaler, Sandra, Author
Saez, Mariel1, Author
Schulze, Felix, Author
Smith, Brian, Author
Seminar, for the Lens, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematics, Analysis of PDEs, math.AP,
 Abstract: We consider convex symmetric lens-shaped networks in R^2 that evolve under 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.

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 Dates: 2007-11-072011
 Publication Status: Issued
 Pages: 29 pages, 5 figures
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 0711.1108
URI: http://arxiv.org/abs/0711.1108
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Title: Transactions of the American Mathematical Society
  Other : Trans. Amer. Math. Soc.
Source Genre: Journal
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Publ. Info: Providence, R.I. : American Mathematical Society
Pages: - Volume / Issue: 363 (5) Sequence Number: - Start / End Page: 2265 - 2294 Identifier: ISSN: 0002-9947
CoNE: https://pure.mpg.de/cone/journals/resource/954925218003