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, p. 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
@article{ASNSP_2004_5_3_4_871_0,
     author = {Kirchheim, Bernd and Serra Cassano, Francesco},
     title = {Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {4},
     year = {2004},
     pages = {871-896},
     zbl = {1170.28300},
     mrnumber = {2124590},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2004_5_3_4_871_0}
}
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://www.numdam.org/item/ASNSP_2004_5_3_4_871_0/

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