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Journal Articles Nonlinear Analysis: Theory, Methods and Applications Year : 2015

Hausdorff volume in non equiregular sub-Riemannian manifolds

Frédéric Jean

Abstract

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).
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hal-01107470 , version 1 (21-01-2015)
hal-01107470 , version 2 (27-06-2015)

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Roberta Ghezzi, Frédéric Jean. Hausdorff volume in non equiregular sub-Riemannian manifolds. Nonlinear Analysis: Theory, Methods and Applications, 2015, 126, pp.345-377. ⟨10.1016/j.na.2015.06.011⟩. ⟨hal-01107470v2⟩
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