Advanced Studies in Pure Mathematics

On a method to disprove generalized Brunn–Minkowski inequalities

Nicolas Juillet

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Abstract

We present a general method to disprove generalized Brunn–Minkowski inequalities. We initially developed this method in [14] in the particular case of the sub-Riemannian Heisenberg group in order to prove that this space does not satisfy a curvature-dimension condition in the sense of Lott–Villani and Sturm.

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 189-198

Dates
Received: 16 January 2009
Revised: 3 September 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086319

Digital Object Identifier
doi:10.2969/aspm/05710189

Mathematical Reviews number (MathSciNet)
MR2648260

Zentralblatt MATH identifier
1216.28007

Subjects
Primary: 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 53C17: Sub-Riemannian geometry

Keywords
Brunn–Minkowski inequality curvature-dimension optimal transport Heisenberg group Grušin plane

Citation

Juillet, Nicolas. On a method to disprove generalized Brunn–Minkowski inequalities. Probabilistic Approach to Geometry, 189--198, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710189. https://projecteuclid.org/euclid.aspm/1543086319


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