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On the Hausdorff volume in sub-Riemannian geometry. (English) Zbl 1236.53030

This paper considers the geometry and analysis in sub-Riemannian spaces, for instance, the Radon-Nikodym derivatives of the spherical Hausdorff measure with respect to a smooth volume. The authors study topics of relative geometric measure theory along with this research, such as tangent measure geometry on sub-Riemannian spaces. They also study some relationships between Hausdorff measures defined on sub-Riemannian spaces and the volume of the unit ball.

MSC:

53C17 Sub-Riemannian geometry
58C35 Integration on manifolds; measures on manifolds
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