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Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies

Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies AbstractThe classical Loomis–Whitney inequality and the uniform cover inequality of Bollobás and Thomason provide upper bounds for the volume of a compact set in terms of its lower dimensional coordinate projections. We provide further extensions of these inequalities in the setting of convex bodies. We also establish the corresponding dual inequalities for coordinate sections; these uniform cover inequalities for sections may be viewed as extensions of Meyer’s dual Loomis–Whitney inequality. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH Berlin/Boston
ISSN
1615-7168
eISSN
1615-7168
DOI
10.1515/advgeom-2017-0063
Publisher site
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Abstract

AbstractThe classical Loomis–Whitney inequality and the uniform cover inequality of Bollobás and Thomason provide upper bounds for the volume of a compact set in terms of its lower dimensional coordinate projections. We provide further extensions of these inequalities in the setting of convex bodies. We also establish the corresponding dual inequalities for coordinate sections; these uniform cover inequalities for sections may be viewed as extensions of Meyer’s dual Loomis–Whitney inequality.

Journal

Advances in Geometry – de Gruyter

Published: Jul 26, 2018

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