Abstract

Extending the well-known characteristic property of solid ellipsoids as convex bodies with hyperplanar shadow-boundaries, we describe all n-dimensional closed convex sets in Rn\mathbb{R}^n whose shadow-boundaries satisfy certain conditions of hyperplanarity.

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

  • Convex
  • body
  • ellipsoid
  • hypersurface
  • sharp shadow-boundary
  • solid
  • quadric

Mathematics Subject Classification

52A20

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Suggested citation

V. Soltan. “Convex Solids with Hyperplanar Shadow-Boundaries.” Journal of Convex Analysis 19 (2012), No. 3, 591–607. https://doi.org/10.68381/jca19033

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.