Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 4, pp. 871-896.

We construct an intrinsic regular surface in the first Heisenberg group 1 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.

Classification: 28A75, 28A78, 22E25
Kirchheim, Bernd 1; Serra Cassano, Francesco 2

1 Dipartimento di Matematica Mathematical Institute University of Oxford 24-29 St Giles’ Oxford, OX1 3LB, UK
2 Dipartimento di Matematica Università di Trento Via Sommarive, 14 38050 Povo (Trento), Italia
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Kirchheim, Bernd; Serra Cassano, Francesco. Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 4, pp. 871-896. http://archive.numdam.org/item/ASNSP_2004_5_3_4_871_0/

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