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Journal Article

Evolution of convex lens-shaped networks under curve shortening flow

MPS-Authors

Saez,  Mariel
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0711.1108
(Preprint), 308KB

TransAMS363-2265.pdf
(Any fulltext), 575KB

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Citation

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.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-093A-4
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.