6533b834fe1ef96bd129ce9a

RESEARCH PRODUCT

Area of intrinsic graphs and coarea formula in Carnot Groups

Antoine JuliaSebastiano Nicolussi GoloDavide Vittone

subject

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

description

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.

yearjournalcountryeditionlanguage
2020-04-06
https://dx.doi.org/10.48550/arxiv.2004.02520