On measures in sub-Riemannian geometry

Abstract : In \cite{gjha} we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim is to extend the study to other kinds of intrinsic measures on sub-Riemannian manifolds, namely Popp's measure and general (i.e., non spherical) Hausdorff measures. The second is to explore some consequences of \cite{gjha} on metric measure spaces based on sub-Riemannian manifolds.
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R Ghezzi, Frédéric Jean. On measures in sub-Riemannian geometry. Séminaire de Théorie Spectrale et Géométrie, Grenoble : Université de Grenoble 1, Institut Fourier, 1983-, 2018, 33 (2015-2016), ⟨10.5802/tsg.312⟩. ⟨hal-01452778v3⟩

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