By Valentino Magnani

We receive an intrinsic Blow-up Theorem for normal hypersurfaces on graded nilpotent teams. This approach permits us to symbolize explicitly the Riemannian floor degree by way of the round Hausdorff degree with admire to an intrinsic distance of the crowd, specifically homogeneous distance. We practice this outcome to get a model of the Riemannian coarea forumula on sub-Riemannian teams, that may be expressed when it comes to arbitrary homogeneous distances.We introduce the typical category of horizontal isometries in sub-Riemannian teams, giving examples of rotational invariant homogeneous distances and rotational teams, the place the coarea formulation takes a less complicated shape. via a similar Blow-up Theorem we receive an optimum estimate for the Hausdorff size of the attribute set relative to C1,1 hypersurfaces in 2-step teams and we turn out that it has finite Q − 2 Hausdorff degree, the place Q is the homogeneous size of the crowd.

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