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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- © Copyright 1989 American Mathematical Society
- 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