Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group

Kirchheim, Bernd; Serra Cassano, Francesco

Geodesic

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Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 4, pp. 871-896

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Résumé

We construct an intrinsic regular surface in the first Heisenberg group $ℍ^{1} \equiv ℝ^{3}$ 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 $\frac{1}{2}$ -Hölder continuous parameterization.

MR Zbl

Classification : 28A75, 28A78, 22E25

Affiliations des auteurs :

Kirchheim, Bernd ¹ ; Serra Cassano, Francesco ²

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     title = {Rectifiability and parameterization of intrinsic regular surfaces in the {Heisenberg} group},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {871--896},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {4},
     year = {2004},
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     zbl = {1170.28300},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_4_871_0/}
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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, Série 5, Tome 3 (2004) no. 4, pp. 871-896. http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_4_871_0/