Geodesic
Characterizations of intrinsic rectifiability in Heisenberg groups
Mattila, Pertti1  ; Serapioni, Raul2  ; Serra Cassano, Francesco2
1 Department of Mathematics and Statistics, University of Helsinki, FI-00014, Finland
2 Dipartimento di Matematica, Università di Trento, Via Sommarive, 14, 38050 Povo (Trento), Italia
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 4, pp. 687-723

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We define rectifiable sets in the Heisenberg groups as countable unions of Lipschitz images of subsets of a Euclidean space, in the case of low-dimensional sets, or as countable unions of subsets of intrinsic C 1 surfaces, in the case of low-codimensional sets. We characterize both low-dimensional rectifiable sets and low codimensional rectifiable sets with positive lower density, in terms of almost everywhere existence of approximate tangent subgroups or of tangent measures.

Classification : 28A75, 28C10

Mattila, Pertti 1 ; Serapioni, Raul 2 ; Serra Cassano, Francesco 2

1 Department of Mathematics and Statistics, University of Helsinki, FI-00014, Finland
2 Dipartimento di Matematica, Università di Trento, Via Sommarive, 14, 38050 Povo (Trento), Italia 
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Mattila, Pertti; Serapioni, Raul; Serra Cassano, Francesco. Characterizations of intrinsic rectifiability in Heisenberg groups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 4, pp. 687-723. http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_4_687_0/