Curves of Finite Total Curvature
Abstract
Description
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.
25 pages, 4 figures; final version, to appear in "Discrete Differential Geometry", Oberwolfach Seminars 38, Birkhauser, 2008
25 pages, 4 figures; final version, to appear in "Discrete Differential Geometry", Oberwolfach Seminars 38, Birkhauser, 2008