Shadow Systems and Volumes of Polar Convex Bodies

It is proved that the reciprocal of the volume of the polar bodies, about the Santalo point, of a shadow system of convex bodies K t , is a convex function of t , thus extending to the non-symmetric case a result of Campi and Gronchi. The case that the reciprocal of the volume is an affine function of t is also investigated and is characterized under certain conditions. These results are applied to prove an exact reverse Santalo inequality for polytopes in ℝ d that have at most d + 3 vertices.

• Publication year

  2006

• Venue

  Mathematika

• Publication date

  2006-06-01

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1112/S0025579300000061arXiv math/0606305
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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