The Second Hull of a Knotted Curve
Geometric Topology
2019-09-16 v2 Differential Geometry
Abstract
The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.
Cite
@article{arxiv.math/0204106,
title = {The Second Hull of a Knotted Curve},
author = {Jason Cantarella and Greg Kuperberg and Rob Kusner and John M Sullivan},
journal= {arXiv preprint arXiv:math/0204106},
year = {2019}
}
Comments
7 pages, 6 figures; final version (only minor changes) to appear in Amer.J.Math