In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter.In particular, given an isodiametric set, and up to negligible sets, we prove that its boundary is given by the graphs of two locally Lipschitz functions.Moreover, in the restricted class of rotationally invariant sets, we give a quite complete characterization of any compact (rotationally invariant) isodiametric set. More specifically, its Steiner symmetrization with respect to the Cn-planeis shown to coincide with the Euclidean convex hull of a CC-ball. At the same time, we also prove quite unexpected non-uniqueness results.

Isodiametric sets in the Heisenberg group / Leonardi, Gian Paolo; Rigot, Severine; Vittone, Davide. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - STAMPA. - 28 (4)(2012), pp. 999-1024.

I documenti presenti in Iris Unimore sono rilasciati con licenza Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia, salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Powered by IRIS-about IRIS-Utilizzo dei cookie

 Copyright © 2021