Convex Solids with Hyperplanar Shadow-Boundaries

Abstract

<jats:p> 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 <jats:inline-formula> <jats:alternatives> <jats:tex-math notation="LaTeX">\mathbb{R}^n</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi mathvariant="double-struck">R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> whose shadow-boundaries satisfy certain conditions of hyperplanarity. </jats:p>