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The Brascamp–Lieb Polyhedron

Published online by Cambridge University Press:  20 November 2018

Stefán Ingi Valdimarsson
Stefán Ingi Valdimarsson*
Affiliation:
UCLA Mathematics Department, Los Angeles, CA, U.S.A. and Science Institute, University of Iceland, Reykjavik, Iceland, e-mail: siv@hi.is
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Abstract

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A set of necessary and sufficient conditions for the Brascamp–Lieb inequality to hold has recently been found by Bennett, Carbery, Christ, and Tao. We present an analysis of these conditions. This analysis allows us to give a concise description of the set where the inequality holds in the case where each of the linear maps involved has co-rank 1. This complements the result of Barthe concerning the case where the linear maps all have rank 1. Pushing our analysis further, we describe the case where the maps have either rank 1 or rank 2.

A separate but related problem is to give a list of the finite number of conditions necessary and sufficient for the Brascamp–Lieb inequality to hold. We present an algorithm which generates such a list.

Keywords

44A3514M1526D20Brascamp–Lieb inequalityLoomis–Whitney inequalitylatticeflag
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 4 , 01 August 2010 , pp. 870 - 888
Copyright
Copyright © Canadian Mathematical Society 2010

References

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