Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
Karoly J. B\"or\"oczky, Ferenc Fodor, Pavlos Kalantzopoulos
TL;DR
This paper characterizes the conditions for equality in Liakopoulos's volume estimate by leveraging Barthe's Reverse Brascamp-Lieb inequality, linking geometric inequalities and subspace sections.
Contribution
It provides a new characterization of equality in Liakopoulos's inequality using Barthe's Reverse Brascamp-Lieb inequality, connecting geometric and functional inequalities.
Findings
Equality cases in Liakopoulos's volume estimate are characterized via Barthe's inequality.
The work links geometric sections with functional inequality conditions.
Provides a new perspective on volume inequalities in geometric analysis.
Abstract
We use the characterization of the case of equality in Barthe's Geometric Reverse Brascamp-Lieb inequality to characterize equality in Liakopoulos's volume estimate in terms of sections by certain lower-dimensional linear subspaces.
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