Hausdorff volume in non equiregular sub-Riemannian manifolds

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give condit...

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Bibliographic Details
Published in:arXiv.org 2015-06
Main Authors: Ghezzi, Roberta, Jean, Frédéric
Format: Article
Language:English
Subjects:
Brownian motion
Radon
Riemann manifold
Online Access:Get full text
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Summary:In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give conditions under which it is a Radon measure. We finally give a complete characterization of the singular part. We illustrate our results and techniques on numerous examples and cases (e.g. to generic sub-Riemannian structures).
ISSN:2331-8422