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

Balogh, Zoltán M., Rickly, Matthieu, and Serra Cassano, Francesco. "Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric.." Publicacions Matemàtiques 47.1 (2003): 237-259. <http://eudml.org/doc/41487>.

@article{Balogh2003,
abstract = {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.},
author = {Balogh, Zoltán M., Rickly, Matthieu, Serra Cassano, Francesco},
journal = {Publicacions Matemàtiques},
keywords = {Distancia de Hausdorff; Dimensión de Hausdorff; Espacio euclídeo; Grupo de Heisenberg; Espacios métricos; Hausdorff measure; Heisenberg metric; rectifiability},
language = {eng},
number = {1},
pages = {237-259},
title = {Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric.},
url = {http://eudml.org/doc/41487},
volume = {47},
year = {2003},
}

TY - JOUR
AU - Balogh, Zoltán M.
AU - Rickly, Matthieu
AU - Serra Cassano, Francesco
TI - Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric.
JO - Publicacions Matemàtiques
PY - 2003
VL - 47
IS - 1
SP - 237
EP - 259
AB - 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.
LA - eng
KW - Distancia de Hausdorff; Dimensión de Hausdorff; Espacio euclídeo; Grupo de Heisenberg; Espacios métricos; Hausdorff measure; Heisenberg metric; rectifiability
UR - http://eudml.org/doc/41487
ER -