We consider submanifolds of sub-Riemannian Carnot groups with intrinsic C 1 regularity. Our first main result is an area formula for C 1 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 C 1 submanifolds into level sets of a C 1 function.
Area of intrinsic graphs and coarea formula in Carnot groups
Julia, Antoine;Nicolussi Golo, Sebastiano
;Vittone, Davide
2022
Abstract
We consider submanifolds of sub-Riemannian Carnot groups with intrinsic C 1 regularity. Our first main result is an area formula for C 1 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 C 1 submanifolds into level sets of a C 1 function.
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