We construct an intrinsic regular surface in the first Heisenberg group equipped wiht its Carnot-Carathéodory metric which has euclidean Hausdorff dimension . Moreover we prove that each intrinsic regular surface in this setting is a -dimensional topological manifold admitting a -Hölder continuous parameterization.
@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}, pages = {871--896}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {4}, year = {2004}, mrnumber = {2124590}, zbl = {1170.28300}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2004_5_3_4_871_0/} }
TY - JOUR AU - Kirchheim, Bernd AU - Serra Cassano, Francesco TI - Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 871 EP - 896 VL - 3 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2004_5_3_4_871_0/ LA - en ID - ASNSP_2004_5_3_4_871_0 ER -
%0 Journal Article %A Kirchheim, Bernd %A Serra Cassano, Francesco %T Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 871-896 %V 3 %N 4 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2004_5_3_4_871_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2004_5_3_4_871_0/
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