We show by explicit estimates that the SubRiemannian distance in a Carnot group of step two is locally semiconcave away from the diagonal if and only if the group does not contain abnormal minimizing curves. Moreover, we prove that local semiconcavity fails to hold in the step-3 Engel group, even in the weaker “horizontal” sense.
On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups / Montanari, Annamaria; Morbidelli, Daniele. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 444:2(2016), pp. 1652-1674. [10.1016/j.jmaa.2016.07.032]
On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups
MONTANARI, ANNAMARIA;MORBIDELLI, DANIELE
2016
Abstract
We show by explicit estimates that the SubRiemannian distance in a Carnot group of step two is locally semiconcave away from the diagonal if and only if the group does not contain abnormal minimizing curves. Moreover, we prove that local semiconcavity fails to hold in the step-3 Engel group, even in the weaker “horizontal” sense.File in questo prodotto:
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