On coincidence of p-module of a family of curves and p-capacity on the Carnot group

Autores: Irina Markina
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 19, Nº 1, 2003, págs. 143-160
Idioma: inglés
DOI: 10.4171/rmi/340
Títulos paralelos:
- Sobre la coincidencia del p-módulo de una familia de curvas y la p-capacidad en el grupo de Carnot
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Resumen
- The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory. In particular, the coincidence of the p-module and the p-capacity plays an mportant role. We consider this problem on the Carnot group. The Carnot group G is a simply connected nilpotent Lie group equipped vith an appropriate family of dilations. Let omega be a bounded domain on G and Ko, K1 be disjoint non-empty compact sets in the closure of omega. We consider two quantities, associated with this geometrical structure...