Search results for " Coarea formula"

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Area of intrinsic graphs and coarea formula in Carnot Groups

2020

AbstractWe consider submanifolds of sub-Riemannian Carnot groups with intrinsic $$C^1$$ C 1 regularity ($$C^1_H$$ C H 1 ). Our first main result is an area formula for $$C^1_H$$ C H 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 $$C^1_H$$ C H 1 submanifolds into level sets of a $$C^1_H$$ C H 1 function.

Mathematics - Differential GeometrySubmanifoldsGeneral MathematicsCarnot groups Area formula Coarea formula Hausdorff measures SubmanifoldsryhmäteoriaCoarea formulaMetric Geometry (math.MG)Area formulaHausdorff measuressubmanifoldsdifferentiaaligeometriacoarea formulaMathematics - Metric GeometryDifferential Geometry (math.DG)Mathematics - Classical Analysis and ODEsCarnot groupsClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric Geometryarea formulamittateoriaMathematics::Differential Geometry53C17 28A75 22E30
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