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Expanding convex immersed closed plane curves. (English) Zbl 1177.35114

Summary: We study the evolution driven by curvature of a given convex immersed closed plane curve. We show that it will converge to a self-similar solution eventually. This self-similar solution may or may not contain singularities. In case it does, we also have estimate on the curvature blow-up rate.

MSC:

35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
53A04 Curves in Euclidean and related spaces
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
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