Displaying similar documents to “Blow-up of regular submanifolds in Heisenberg groups and applications”

Some properties of Carnot-Carathéodory balls in the Heisenberg group

Roberto Monti (2000)

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

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Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. ∇ H n ⁡ d ⁢ z , t = 1 in the classical sense for all z , t ∈ H n with z ≠ 0 , where d is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.

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 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).