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

• Autores: Zoltán M. Balogh, Francesco Serra Cassano, Matthieu Rickly
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 47, Nº 1, 2003, págs. 237-259
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.