Shadow systems and volumes of polar convex bodies
نویسندگان
چکیده
We prove that the reciprocal of the volume of the polar bodies, about the Santaló point, of a shadow system of convex bodies Kt, 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. We apply these results to prove exact reverse Santaló inequality for polytopes in R that have at most d + 3 vertices.
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