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The second hull of a knotted curve
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 125, Number 6, December 2003
- pp. 1335-1348
- 10.1353/ajm.2003.0038
- Article
- Additional Information
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.