Remarks on Gaussian-stability for Brascamp--Lieb Inequalities
Jonathan Bennett, Michael Christ
TL;DR
This paper proves a stable version of the Euclidean Brascamp-Lieb inequality for exponents between 1 and 2, showing that near-extremizers are close to Gaussian functions, thus advancing understanding of the inequality's stability.
Contribution
It establishes a stable form of the Brascamp-Lieb inequality for a broad range of exponents, demonstrating that near-extremizers are approximately Gaussian.
Findings
Near-extremizers are nearly Gaussian functions.
The stability result holds for all cases with exponents between 1 and 2.
The paper extends the understanding of the structure of extremizers in Brascamp-Lieb inequalities.
Abstract
We establish a stable form of the general Euclidean Brascamp-Lieb inequality in all cases in which the Lebesgue exponents are strictly between 1 and 2, asserting that all near-extremizers are nearly Gaussian.
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Taxonomy
TopicsGeometry and complex manifolds · Nonlinear Partial Differential Equations · Numerical methods in inverse problems