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

Geometric functional analysis and applications November 13, 2017 - November 17, 2017

November 17, 2017 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Apostolos Giannopoulos (National and Kapodistrian University of Athens (University of Athens))
Location: MSRI: Simons Auditorium
Tags/Keywords
  • convex bodies

  • volume of projections and sections

  • Loomis-Whitney inequality

  • uniform cover inequality

  • surface area

  • average section functional

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

20-Giannopoulos

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. Joint work with S. Brazitikos and D-M. Liakopoulos. We also discuss applications of these inequalities to questions regarding the surface area of lower dimensional projections and the average section functional of lower dimensional sections of a convex body, which were the motivation for them (joint works with A. Koldobsky, S. Dann, S. Brazitikos and P. Valettas).

Supplements
30108?type=thumb Giannopoulos Notes 1.36 MB application/pdf Download
Video/Audio Files

20-Giannopoulos

H.264 Video 20-Giannopoulos.mp4 402 MB video/mp4 rtsp://videos.msri.org/data/000/030/035/original/20-Giannopoulos.mp4 Download
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