2002/04/30 by Jason Cantarella, Greg Kuperberg, Rob Kusner +3 · 2 citations
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DG #math.GT #msc:49Q10 #msc:52A30 #msc:53A04 #msc:57M25
paper · pdf · doi:10.1353/ajm.2003.0038
published as Amer. J. Math. 125 (2003), 1335-1348 · 7 pages, 6 figures; final version (only minor changes) to appear in Amer.J.Math
arxiv created 2003/03/26 · openalex publication_date 2003/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11 · arxiv updated 2026/08/03
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 Fáry/Milnor theorem that every knotted curve has total curvature at least 4π.