Regular submanifolds, graphs and area formula in Heisenberg groups

• Autores: B. Franchi, Raul Serapioni, Francesco Serra Cassano
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 211, Nº 1, 2007, págs. 152-203
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.07.015
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• Resumen

  • We describe intrinsically regular submanifolds in Heisenberg groups H. Low dimensional and low codimensional submanifolds turn out to be of a very different nature. The first ones are Legendrian surfaces, while low codimensional ones are more general objects, possibly non-Euclidean rectifiable. Nevertheless we prove that they are graphs in a natural group way, as well as that an area formula holds for the intrinsic Hausdorff measure. Finally, they can be seen as Federer¿Fleming currents given a natural complex of differential forms on H