The affine curve-lengthening flow

Ben Andrews

doi:10.1515/crll.1999.008

The affine curve-lengthening flow

Ben Andrews^*

^*Corresponding author for this work

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

40 Citations (Scopus)

Abstract

The motion of any smooth closed convex curve in the plane in the direction of steepest increase of its affine arc length can be continued smoothly for all time. The evolving curve remains strictly convex while expanding to infinite size and approaching a homothetically expanding ellipse.

Original language	English
Pages (from-to)	43-83
Number of pages	41
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	506
DOIs	https://doi.org/10.1515/crll.1999.008
Publication status	Published - 1999

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title = "The affine curve-lengthening flow",

abstract = "The motion of any smooth closed convex curve in the plane in the direction of steepest increase of its affine arc length can be continued smoothly for all time. The evolving curve remains strictly convex while expanding to infinite size and approaching a homothetically expanding ellipse.",

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year = "1999",

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language = "English",

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DO - 10.1515/crll.1999.008

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JO - Journal fur die Reine und Angewandte Mathematik

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The affine curve-lengthening flow

Abstract

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