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

DOI:
https://doi.org/10.1090/S0002-9947-1989-0989580-5

MathSciNet review:
989580

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-1989-0989580-5

Keywords:
Curve straightening,
total squared curvature,
gradient flow

Article copyright:
© Copyright 1989
American Mathematical Society