# Evolution of convex lens-shaped networks under the curve shortening flow

@article{Schnurer2007EvolutionOC, title={Evolution of convex lens-shaped networks under the curve shortening flow}, author={Oliver C. Schnurer and Abderrahim Azouani and M Dimirovski Georgi and Juliette Hell and Nihar Jangle and Amos Nathan Koeller and Tobias Marxen and Sandra Ritthaler and Mariel S'aez and Felix Schulze and Brian T. Smith and for the Lens Seminar}, journal={Transactions of the American Mathematical Society}, year={2007}, volume={363}, pages={2265-2294} }

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.

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