On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

关键词: Carnot groups;    SubRiemannian distance;    Abnormal curve;    Semiconcavity;   

DOI  :  10.1016/j.jmaa.2016.07.032

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free