A comparison of Euclidean and Heisenberg Hausdorff measures

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Mattila , P E J & Venieri , L 2019 , ' A comparison of Euclidean and Heisenberg Hausdorff measures ' , Revista Matematica Iberoamericana , vol. 35 , no. 5 , pp. 1485–1500 . https://doi.org/10.4171/RMI/1089

Title: A comparison of Euclidean and Heisenberg Hausdorff measures
Author: Mattila, Pertti Esko Juhani; Venieri, Laura
Contributor organization: Department of Mathematics and Statistics
Date: 2019
Language: eng
Number of pages: 16
Belongs to series: Revista Matematica Iberoamericana
ISSN: 0213-2230
DOI: https://doi.org/10.4171/RMI/1089
URI: http://hdl.handle.net/10138/306960
Abstract: We prove some geometric properties of sets in the first Heisenberg group whose Heisenberg Hausdorff dimension is the minimal or maximal possible in relation to their Euclidean one and the corresponding Hausdorff measures are positive and finite. In the firs, case we show that these sets must be in a sense horizontal and in the second case vertical. We show the sharpness of our results with some examples.
Subject: 111 Mathematics
Hausdorff measure
Heisenberg group
Hausdorff dimension
FRACTALS
Hausdorff measure
Heisenberg group
Hausdorff dimension
FRACTALS
Peer reviewed: Yes
Rights: cc_by
Usage restriction: openAccess
Self-archived version: acceptedVersion


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