The case of equality in geometric instances of Barthe's reverse Brascamp-Lieb inequalit
Karoly J. Boroczky, Pavlos Kalantzopoulos, Dongmeng Xi
TL;DR
This paper characterizes the conditions for equality in the geometric case of Barthe's reverse Brascamp-Lieb inequality, building on prior work that identified equality cases in the forward inequality.
Contribution
It provides a complete characterization of equality in the geometric case of Barthe's reverse Brascamp-Lieb inequality, extending previous results on the forward inequality.
Findings
Identifies conditions for equality in the reverse inequality
Extends known results from the forward to the reverse case
Clarifies the structure of extremizers in the geometric setting
Abstract
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe's reverse Brascamp-Lieb inequality.
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Taxonomy
TopicsGeometric and Algebraic Topology · Point processes and geometric inequalities · Homotopy and Cohomology in Algebraic Topology