Evolution of convex lens-shaped networks under curve shortening flow
Differential Geometry
2019-08-14 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.0711.1108,
title = {Evolution of convex lens-shaped networks under curve shortening flow},
author = {Oliver C. Schnürer and Abderrahim Azouani and Marc Georgi and Juliette Hell and Nihar Jangle and Amos Koeller and Tobias Marxen and Sandra Ritthaler and Mariel Sáez and Felix Schulze and Brian Smith},
journal= {arXiv preprint arXiv:0711.1108},
year = {2019}
}
Comments
29 pages, 5 figures