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.
@article{urn:eudml:doc:41487,
title = {Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric.},
journal = {Publicacions Matem\`atiques},
volume = {47},
year = {2003},
pages = {237-259},
zbl = {1060.28002},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41487}
}
Balogh, Zoltán M.; Rickly, Matthieu; Serra Cassano, Francesco. Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric.. Publicacions Matemàtiques, Tome 47 (2003) pp. 237-259. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41487/