Abstract:
We study the metric properties of level surfaces for classes of smooth noncontact mappings from arbitrary Carnot groups into two-step ones with some constraints on the dimensions of horizontal subbundles and the subbundles corresponding to degree 2 fields. We calculate the Hausdorff dimension of the level surfaces with respect to the sub-Riemannian quasimetric and derive an analytical relation between the Hausdorff measures for the sub-Riemannian quasimetric and the Riemannian metric. As application, we establish a new form of coarea formula, also proving that the new coarea factor is well defined.
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