Curves of Finite Total Curvature
John M Sullivan
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.
Create a lesson
Related papers
Mapping class groups have a unique Polish group structure
Tyrone Ghaswala, Sumun Iyer, Robert Alonzo Lyman et al.
Around the Andreadakis-Johnson filtration
Yusuke Kuno
Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology
Huize Jin
A note on surfaces with large systoles
Yifei Cai
Real ideal points, Conway spheres, and left-orderable Dehn fillings
Yi Wang
All once-extended 3D TQFTs are Reshetikhin--Turaev theories
Glen Lim