Non-convergence and instability in the asymptotic behaviour of curves evolving by curvature

Ben Andrews

doi:10.4310/CAG.2002.v10.n2.a8

Non-convergence and instability in the asymptotic behaviour of curves evolving by curvature

Ben Andrews

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We consider curvature-driven evolution equations for curves in the plane, and prove that the isoperimetric ratios of the evolving curves generically approach infinity if the speed of motion is proportional to curvature to a power less than 1/3.

Original language	English
Pages (from-to)	409-449
Number of pages	41
Journal	Communications in Analysis and Geometry
Volume	10
Issue number	2
DOIs	https://doi.org/10.4310/CAG.2002.v10.n2.a8
Publication status	Published - Apr 2002

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abstract = "We consider curvature-driven evolution equations for curves in the plane, and prove that the isoperimetric ratios of the evolving curves generically approach infinity if the speed of motion is proportional to curvature to a power less than 1/3.",

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DO - 10.4310/CAG.2002.v10.n2.a8

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JO - Communications in Analysis and Geometry

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Non-convergence and instability in the asymptotic behaviour of curves evolving by curvature

Abstract

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