Differentiability of mappings in the geometry of Carnot manifolds

• Autores: S. K. Vodopyanov
• Localización: Siberian mathematical journal, ISSN 0037-4466, Vol. 48, Nº. 2, 2007, págs. 197-213
• Idioma: inglés
• DOI: 10.1007/s11202-007-0022-4
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• Resumen

  • We study the differentiability of mappings in the geometry of Carnot-Carathéodory spaces under the condition of minimal smoothness of vector fields. We introduce a new concept of hc-differentiability and prove the hc-differentiability of Lipschitz mappings of Carnot-Carathéodory spaces (a generalization of Rademacher¿s theorem) and a generalization of Stepanov¿s theorem. As a consequence, we obtain the hc-differentiability almost everywhere of the quasiconformal mappings of Carnot-Carathéodory spaces. We establish the hc-differentiability of rectifiable curves by way of proof. Moreover, the paper contains a new proof of the functorial property of the correspondence a local basis [] the nilpotent tangent cone.