The Second Hull of a Knotted Curve
  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. 
Jason Cantarella (Univ Georgia), Greg Kuperberg (UC Davis), Rob Kusner   (UMass/Amherst), John M Sullivan (Univ Illinois)