| Evolution of convex lens-shaped networks under curve shortening flow (2007) | |||||||||
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.. Comment: 29 pages, 5 figures | |||||||||
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