Displaying similar documents to “Rectifiability and perimeter in step 2 Groups”

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

Similarity:

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

Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group

Bernd Kirchheim, Francesco Serra Cassano (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We construct an intrinsic regular surface in the first Heisenberg group ℍ 1 ≡ ℝ 3 equipped wiht its Carnot-Carathéodory metric which has euclidean Hausdorff dimension  2 . 5 . Moreover we prove that each intrinsic regular surface in this setting is a 2 -dimensional topological manifold admitting a 1 2 -Hölder continuous parameterization.

Some relations among volume, intrinsic perimeter and one-dimensional restrictions of B V functions in Carnot groups

Francescopaolo Montefalcone (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Let 𝔾 be a k -step Carnot group. The first aim of this paper is to show an interplay between volume and 𝔾 -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for 𝔾 -regular submanifolds of codimension one. We then give some applications of this result: slicing of B V 𝔾 functions, integral geometric formulae for volume and 𝔾 -perimeter and, making use of a suitable notion of convexity, called, we state a Cauchy type formula for 𝔾 -convex sets. Finally,...