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

Rectifiability and perimeter in step 2 Groups

Bruno Franchi, Raul Serapioni, Francesco Serra Cassano (2002)

Mathematica Bohemica

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We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).

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

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

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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.