# A comparison of Euclidean and Heisenberg Hausdorff measures

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http://hdl.handle.net/10138/306960

#### Citation

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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