Curves of Finite Total Curvature

2006/06/01 by John M. Sullivan, Sullivan, John M · 1 citation
Engineering · #26A45 (Secondary) #53A04 (Primary) #53C65 #57M25 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.math/0606007

openalex publication_date 2006/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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