The Space of Minimal Annuli Bounded by an Extremal Pair of Planar Curves
نویسندگان
چکیده
In 1956 Shiffman [14] proved that every minimally immersed annulus in 3 bounded by convex curves in parallel planes is embedded. He proved this theorem by showing that the minimal annulus was foliated by convex curves in parallel planes. We are able to prove a related embeddedness theorem for extremal convex planar curves. Recall that a subset of 3 is extremal if it is contained on the boundary of its convex hull. We will call a pair of convex curves extremal if their union is extremal.
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