Minimal Surfaces Bounded by Convex Curves in Parallel Planes

@inproceedings{Meeks1991MinimalSB,
  title={Minimal Surfaces Bounded by Convex Curves in Parallel Planes},
  author={PlanesWilliam H. Meeks},
  year={1991}
}
  • PlanesWilliam H. Meeks
  • Published 1991
In 1956 M. Shiffman [17] proved several beautiful theorems concerning the geometry of a minimal annulus A whose boundary consists of two closed convex curves in parallel planes P1, P2. The first theorem stated that the intersection of A with any plane P , between P1 and P2, is a convex Jordan curve. In particular it follows that A is embedded. He then used this convexity theorem to prove that every symmetry of the boundary of A extended to a symmetry of A. In the case that ∂A consists of two… CONTINUE READING

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