Revista Matemática Iberoamericana


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Volume 27, Issue 2, 2011, pp. 645–732
DOI: 10.4171/RMI/650

Published online: 2011-08-31

Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius

Brian Street[1]

(1) University of Wisconsin, Madison, USA

We study multi-parameter Carnot-Carathéodory balls, generalizing results due to Nagel, Stein and Wainger in the single parameter setting. The main technical result is seen as a uniform version of the theorem of Frobenius. In addition, we study maximal functions associated to certain multi-parameter families of Carnot-Carathéodory balls.

Keywords: Sub-Riemannian geometry, Carnot-Carathéodory geometry, Frobenius theorem, multi-parameter, spaces of homogeneous type, maximal functions

Street Brian: Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius. Rev. Mat. Iberoamericana 27 (2011), 645-732. doi: 10.4171/RMI/650