A comparison of Euclidean and Heisenberg Hausdorff measures

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Sammanfattning

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.

Originalspråkengelska
TidskriftRevista Matematica Iberoamericana
Volym35
Nummer5
Sidor (från-till)1485–1500
Antal sidor16
ISSN0213-2230
DOI
StatusPublicerad - 2019
MoE-publikationstypA1 Tidskriftsartikel-refererad

Vetenskapsgrenar

  • 111 Matematik

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