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:  02132230 
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 
Selfarchived version:  acceptedVersion 
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