We establish an area formula for the spherical measure of intrinsically regular submanifolds of low codimension in Heisenberg groups. The spherical measure is computed with respect to an arbitrary homogeneous distance. Among the arguments of the proof, we point out the differentiability properties of intrinsic graphs and a chain rule for intrinsic differentiable functions.
In this paper we study intrinsic regular submanifolds of H n of low codimension in relation with the regularity of their intrinsic parametrization. We extend some results proved for H-regular surfaces of codimension 1 to H-regular surfaces of codimension k, with 1 ≤ k ≤ n. We characterize uniformly intrinsic differentiable functions, φ, acting between two complementary subgroups of the Heisenberg group H n , with target space horizontal of dimension k, in terms of the Euclidean regularity of their components with respect to a family of non linear vector fields ∇ φj . Moreover, we show how the area of the intrinsic graph of φ can be computed in terms of the components of the matrix representing the intrinsic differential of φ.
In this paper we study intrinsic regular submanifolds of H n , of low co-dimension in relation with the regularity of their intrinsic parametrization. We extend some results proved for one co-dimensional H-regular surfaces, characterizing uniformly intrinsic differentiable functions φ acting between two complementary subgroups of the Heisenberg group H n , with target space horizontal of dimension k, with 1 ≤ k ≤ n, in terms of the Euclidean regularity of its components with respect to a family of non linear vector fields ∇ φ j . Moreover, we show how the area of the intrinsic graph of φ can be computed through the component of the matrix identifying the intrinsic differential of φ.
We establish an area formula for the spherical measure of intrinsically
regular submanifolds of low codimension in Heisenberg groups.
The spherical measure is constructed by an arbitrary homogeneous distance.
Among the arguments of the proof, we point out the differentiability properties of intrinsic graphs and a chain rule for intrinsically differentiable functions.
We prove a coarea-type inequality for a continuously Pansu differentiable function acting between two Carnot groups endowed with homogeneous distances. We assume that the level sets of the function are uniformly lower Ahlfors regular and that the Pansu differential is everywhere surjective.Résumé. -Nous démontrons une inégalité de type co-aire pour une fonction entre deux groupes de Carnot munis de distances homogènes. On suppose que la fonction est continûment différentiable au sens de Pansu avec différentielle continue. On suppose aussi que les ensembles de niveau de la fonction sont uniformément inférieurement Ahlfors-réguliers, et que la différentielle de Pansu est partout surjective.
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