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Hadamard’s Characterization of the Ovaloids

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1000)

Abstract

If p and q are points in En, then \( \overline {pq} \) denotes the line segment between p and q. A set S ⊂ En is convex if for every p ∈ S and q ∈ S, \( \overline {pq} \) ⊂S. A convex body is a compact convex set with a non-empty interior. It is easy to show that a convex body is homeomorphic to a solid sphere (but we will not need this fact). In these notes we will assume in addition that the boundary surface of a convex body in E3 is several times differentiable.

Keywords

  • Line Segment
  • Convex Body
  • Function Element
  • Arbitrary Point
  • Boundary Surface

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1983 Springer-Verlag Berlin Heidelberg

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Hopf, H. (1983). Hadamard’s Characterization of the Ovaloids. In: Differential Geometry in the Large. Lecture Notes in Mathematics, vol 1000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21563-0_9

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  • DOI: https://doi.org/10.1007/978-3-662-21563-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12004-9

  • Online ISBN: 978-3-662-21563-0

  • eBook Packages: Springer Book Archive