Stability for Borell-Brascamp-Lieb inequalities

2016/07/19 by Rossi, Andrea, Salani, Paolo · 3 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1607.05668

Abstract

We study stability issues for the so-called Borell-Brascamp-Lieb inequalities, proving that when near equality is realized, the involved functions must be L¹-close to be p-concave and to coincide up to homotheties of their graphs.

Cited by

• Sharp stability in hypercontractivity estimates and logarithmic Sobolev inequalities
• Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
• A parabolic PDE-based approach to Borell–Brascamp–Lieb inequality

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