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
DOI: 10.5565/publmat_47103_11
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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.