Publication Date:
2015-09-19
Description:
We prove that if $\mu $ is a Radon measure on the Heisenberg group $\mathbb {H}^n$ such that the density $\Theta ^s(\mu ,\cdot )$ , computed with respect to the Korányi metric $d_H$ , exists and is positive and finite on a set of positive $\mu $ measure, then $s$ is an integer. The proof relies on an analysis of uniformly distributed measures on $(\mathbb {H}^n,d_H)$ . We provide a number of examples of such measures, illustrating both the similarities and the striking differences of this sub-Riemannian setting from its Euclidean counterpart.
Print ISSN:
0024-6093
Electronic ISSN:
1469-2120
Topics:
Mathematics
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