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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some properties of the curve straightening flow in the plane


Author: Anders Linnér
Journal: Trans. Amer. Math. Soc. 314 (1989), 605-618
MSC: Primary 58E10; Secondary 53A04, 53C22, 58F17
MathSciNet review: 989580
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Abstract: We will explicitly compute the gradient of the total squared curvature functional on a space of closed curves. An example shows that the flow along the gradient trajectory may cause curves to develop self-intersections. We prove the existence of strictly convex curves that momentarily turn nonconvex. In conclusion we use computer graphics to illustrate how self-intersections come about.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0989580-5
PII: S 0002-9947(1989)0989580-5
Keywords: Curve straightening, total squared curvature, gradient flow
Article copyright: © Copyright 1989 American Mathematical Society