Evolution of convex lens-shaped networks under curve shortening flow
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classification
math.DG
math.AP
keywords
networksconvexappropriatecurveflowlens-shapedself-similarlyshortening
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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.
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