Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group

• Bernd Kirchheim ^[1] ; Francesco Serra Cassano ^[2]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
  2. [2] Università di Trento, Italia
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 3, Nº 4, 2004, págs. 871-896
• Idioma: inglés
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• Resumen

  • Abstract. We construct an intrinsic regular surface in the first Heisenberg group H1 ≡ R3 equipped wiht its Carnot-Carathe´odory 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 -Ho¨ lder con-tinuous parameterization.