Calculus of Variations and Geometric Measure Theory
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Z. Balogh - M. Rickly - F. Serra Cassano

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

created on 20 Dec 2002
modified on 29 Nov 2003


Published Paper

Inserted: 20 dec 2002
Last Updated: 29 nov 2003

Journal: Publ. Mat.
Volume: 47
Number: 1
Pages: 237-259
Year: 2003


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 giv

Keywords: Hausdorff measures, Heisenberg group, Eucildean and $H$- rectifiability

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