Some properties of the curve straightening flow in the plane

Linnér, Anders

doi:10.1090/S0002-9947-1989-0989580-5

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: 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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