The Second Hull of a Knotted Curve

Jason Cantarella; Greg Kuperberg; Rob Kusner; John M Sullivan

doi:10.1353/ajm.2003.0038

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The Second Hull of a Knotted Curve

Jason Cantarella·Greg Kuperberg·Rob Kusner·John M Sullivan

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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.

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Jason Cantarella, Greg Kuperberg, Rob Kusner, John M Sullivan. 2002-04-10. The Second Hull of a Knotted Curve. https://doi.org/10.1353/ajm.2003.0038

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