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Journal of Convex Analysis 19 (2012), No. 3, 591--607
Copyright Heldermann Verlag 2012

Convex Solids with Hyperplanar Shadow-Boundaries

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

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 whose shadow-boundaries satisfy certain conditions of hyperplanarity.

Keywords: Convex, body, ellipsoid, hypersurface, sharp shadow-boundary, solid, quadric.

MSC: 52A20

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