Search results for " Area formula"

showing 2 items of 2 documents

Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets

2013

We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group. peerReviewed

Discrete mathematicsMathematics::Functional AnalysisProperty (philosophy)General Mathematicsmetric area formulata111Mathematics::Analysis of PDEsCarnot groupBanach homogeneous groupsalmost everywhere differentiabilityRadon-Nikodym propertyLipschitz continuityRadon–Nikodym theoremBanach homogeneous groups; metric area formula; almost everywhere differentiability; Radon-Nikodym propertyMetric (mathematics)Homogeneous groupMathematics::Metric GeometryAlmost everywhereDifferentiable functionMathematics
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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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