Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric

We compare the Hausdorff measures and dimensions with respect to the Euclidean and Heisenberg metrics on the first Heisenberg group. The result is a dimension jump described by two inequalities. The sharpness of our estimates is shown by examples. Moreover a comparison between Euclidean and H-rectif...

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Detalles Bibliográficos
Autores: Balogh, Zoltán M., Rickly, Matthieu, Serra Cassano, Francesco
Tipo de recurso: artículo
Fecha de publicación:2003
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:2005
Acceso en línea:https://ddd.uab.cat/record/2005
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_47103_11
Access Level:acceso abierto
Palabra clave:Hausdorff measures
Hausdorff dimension
Heisenberg metric
Descripción
Sumario:We compare the Hausdorff measures and dimensions with respect to the Euclidean and Heisenberg metrics on the first Heisenberg group. The result is a dimension jump described by two inequalities. The sharpness of our estimates is shown by examples. Moreover a comparison between Euclidean and H-rectifiability is given.