Displaying similar documents to “Some properties of Carnot-Carathéodory balls in the Heisenberg group”

Blow-up of regular submanifolds in Heisenberg groups and applications

Valentino Magnani (2006)

Open Mathematics

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We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak...

On some recent developments of the theory of sets of finite perimeter

Luigi Ambrosio (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we describe some recent progress on the theory of sets of finite perimeter, currents, and rectifiability in metric spaces. We discuss the relation between intrinsic and extrinsic theories for rectifiability

Geodesics in the Heisenberg Group

Piotr Hajłasz, Scott Zimmerman (2015)

Analysis and Geometry in Metric Spaces

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We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.

Sets of finite perimeter associated with vector fields and polyhedral approximation

Francescopaolo Montefalcone (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let X = X 1 , ⋯ , X m be a family of bounded Lipschitz continuous vector fields on R n . In this paper we prove that if E is a set of finite X -perimeter then his X -perimeter is the limit of the X -perimeters of a sequence of euclidean polyhedra approximating E in L 1 -norm. This extends to Carnot-Carathéodory geometry a classical theorem of E. De Giorgi.