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Area of intrinsic graphs and coarea formula in Carnot Groups (2004.02520v1)
Published 6 Apr 2020 in math.CA, math.DG, and math.MG
Abstract: We consider submanifolds of sub-Riemannian Carnot groups with intrinsic $C1$ regularity ($C1_H$). Our first main result is an area formula for $C1_H$ intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing $C1_H$ submanifolds into level sets of a $C1_H$ function.