Hadamard’s Characterization of the Ovaloids

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.KeywordsLine SegmentConvex BodyFunction ElementArbitrary PointBoundary SurfaceThese 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.