Evolution of convex lens-shaped networks under curve shortening flow

Schnürer, Oliver C.; Azouani, Abderrahim; Georgi, Marc; Hell, Juliette; Jangle, Nihar; Koeller, Amos; Marxen, Tobias; Ritthaler, Sandra; Saez, Mariel; Schulze, Felix; Smith, Brian; Seminar, for the Lens

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

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;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

0711.1108
(Preprint), 308KB

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

Supplementary Material (public)

There is no public supplementary material available

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.