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math.CA2018
Geometric properties of extremal sets for the dimension comparison in Carnot groups of step 2
Laura Venieri
In Carnot groups of step 2 we consider sets having maximal or minimal possible homogeneous Hausdorff dimension compared to their Euclidean one: in the first case we prove that they…
math.CA2017
A comparison of Euclidean and Heisenberg Hausdorff measures
Pertti Mattila, Laura Venieri
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…
math.CA2017
Dimension estimates for Kakeya sets defined in an axiomatic setting
Laura Venieri
In this dissertation we define a generalization of Kakeya sets in certain metric spaces. Kakeya sets in Euclidean spaces are sets of zero Lebesgue measure containing a segment of l…