Curves of Finite Total Curvature

By John M. Sullivan Jr.. 2006

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We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it includes both smooth and polygonal curves, its study shows us connections between discrete and differential geometry. To explore these ideas, we consider theorems of Fary/Milnor, Schur, Chakerian and Wienholtz.

Subfields: Applied Mathematics, Computational Mechanics, Geometry and Topology

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