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Advances in Geometry

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Volume 18, Issue 3

Issues

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

Silouanos Brazitikos
  • Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis 157-84, Athens, Greece
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/ Apostolos Giannopoulos
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  • Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis 157-84, Athens, Greece
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/ Dimitris-Marios Liakopoulos
  • Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis 157-84, Athens, Greece
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Published Online: 2018-01-24 | DOI: https://doi.org/10.1515/advgeom-2017-0063

Abstract

The 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.

Keywords: Convex bodies; volume of projections and sections; Loomis–Whitney inequality; uniform cover inequality

MSC 2010: Primary 52A20; Secondary 52A23, 52A40, 46B06

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About the article


Received: 2016-06-12

Published Online: 2018-01-24

Published in Print: 2018-07-26


Citation Information: Advances in Geometry, Volume 18, Issue 3, Pages 345–354, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0063.

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