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Search: All articles in the CJM digital archive with keyword Loomis-Whitney inequality

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1. CJM 2010 (vol 62 pp. 870)

Valdimarsson, Stefán Ingi
The Brascamp-Lieb Polyhedron
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:Brascamp-Lieb inequality, Loomis-Whitney inequality, lattice, flag
Categories:44A35, 14M15, 26D20

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