Step-\(s\) involutive families of vector fields, their orbits and the Poincaré inequality
type: Item
instance of: scholarly article
title: Step-\(s\) involutive families of vector fields, their orbits and the Poincaré inequality
zbMATH Open document ID: 1287.53027
author: Annamaria Montanari
author: Daniele Morbidelli
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2013-12-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1106.2410
review text: The authors extend basic machinery of sub-Riemannian geometric analysis to families of vector fields lacking the requisite smoothness necessary for application of Hörmander's classical theorem. They consider families of Euclidean vector fields of class \(C^s\) whose commutators satisfy (somewhat technical) regularity hypotheses. For such families, they establish (i) a ball-box theorem for a suitable almost exponential map, (ii) a doubling property for the Lebesgue measure of control balls, and (iii) an appropriate Poincaré inequality. A key technical complication in their arguments involves injectivity of the almost exponential map, which cannot be obtained by standard methods.
reviewed by: Jeremy T. Tyson
Mathematics Subject Classification ID: 53C17
zbMATH DE Number: 6238888
zbMATH Keywords: Carnot-Carathéodory distance
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: involutivity
zbMATH Keywords: Hörmander vector field
MaRDI profile type: Publication
OpenAlex ID: W3104948975
arXiv ID: 1106.2410
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DOI: 10.1016/J.MATPUR.2012.09.005
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description: scientific article; zbMATH DE number 6238888