Sub-Riemannian structures do not satisfy Riemannian Brunn–Minkowski inequalities

Nicolas Juillet ^[1]
1. [1] University of Strasbourg
  
  University of Strasbourg
  
  Arrondissement de Strasbourg-Ville, Francia
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 1, 2021, págs. 177-188
Idioma: inglés
DOI: 10.4171/rmi/1205
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Resumen
- We prove that no Brunn–Minkowski inequality from the Riemannian theories of curvature-dimension and optimal transportation can be satisfied by a strictly sub-Riemannian structure. Our proof relies on the same method as for the Heisenberg group together with new investigations by Agrachev, Barilari and Rizzi on ample normal geodesics of sub-Riemannian structures and the geodesic dimension attached to them.