Abstract

Extending a well-known characteristic property of ellipsoids, we describe all convex solids K⊂RnK \subset \mathbb{R}^n, possibly unboun\-ded, with the following property: for any vector z∈Rnz \in \mathbb{R}^n and any scalar λ≠0\lambda \ne 0 such that K≠z+λKK \ne z + \lambda K, the intersection of the boundaries of KK and z+λKz + \lambda K lies in a hyperplane. This property is related to hyperplanarity of shadow-boundaries of KK and central symmetricity of small 2-dimensional sections of KK.

Author information

Contact details are reproduced from the original publication and may be historical.

Valeriu Soltan

Dept. of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, U.S.A.

vsoltan@gmu.edu

Keywords

  • Besicovitch
  • body
  • convex
  • ellipse
  • ellipsoid
  • convex
  • quadric
  • section
  • shadow-boundary
  • solid

Mathematics Subject Classification

52A20

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Suggested citation

V. Soltan. “Convex Hypersurfaces with Hyperplanar Intersections of Their Homothetic Copies.” Journal of Convex Analysis 22 (2015), No. 1, 145–159. https://doi.org/10.68381/jca22008

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.