Shadow Systems and Volumes of Polar Convex Bodies
By Mathieu Meyer, Shlomo Reisner. 2006
79 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/b7e474bf85245b0cf7519ec957e20fdd3540514e
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In Applied Mathematics
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- Yiming Zhao
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- Gaoyong Zhang
- Erwin Lutwak
- Deping Ye
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In Molecular Biology
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Citations in the corpus
- Shadow systems of asymmetric Lp zonotopes (2013, methodology): “This result has been extended to the general non-symmetric case by Meyer and Reisner [33].”
- A volume inequality for polar bodies (2010, background): “Recently, Meyer and Reisner [40] have proved inequality (1) for polytopes with at most n+ 3 vertices.”
- The volume product of convex bodies with many hyperplane symmetries (2013, methodology): “The conjecture was proved by Reisner [21] for zonoids (see also [8] for a simple proof) and by Meyer and Reisner [17] for polytopes with less than n+ 3 vertices.”