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Search: All articles in the CJM digital archive with keyword Brunn-Minkowski inequality

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1. CJM Online first

Carlen, Eric; Maggi, Francesco
Stability for the Brunn-Minkowski and Riesz rearrangement inequalities, with applications to Gaussian concentration and finite range non-local isoperimetry
We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the Brunn-Minkowski inequality (for Minkowski sums between generic sets and convex sets) and of the Gaussian concentration inequality. The former inequality is then used to obtain a robust improvement of the Riesz rearrangement inequality under certain natural conditions. These conditions are compatible with the applications to a finite-range nonlocal isoperimetric problem arising in statistical mechanics.

Keywords:Brunn-Minkowski inequality, Riesz rearrangement, Gaussian Concentration, Gates-Penrose-Lebowitz energy

2. CJM 1999 (vol 51 pp. 449)

Bahn, Hyoungsick; Ehrlich, Paul
A Brunn-Minkowski Type Theorem on the Minkowski Spacetime
In this article, we derive a Brunn-Minkowski type theorem for sets bearing some relation to the causal structure on the Minkowski spacetime $\mathbb{L}^{n+1}$. We also present an isoperimetric inequality in the Minkowski spacetime $\mathbb{L}^{n+1}$ as a consequence of this Brunn-Minkowski type theorem.

Keywords:Minkowski spacetime, Brunn-Minkowski inequality, isoperimetric inequality
Categories:53B30, 52A40, 52A38

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