论文标题
Carnot组中有关子鳍指标的变分问题
Variational problems concerning sub-Finsler metrics in Carnot groups
论文作者
论文摘要
本文专门研究在给定卡诺组的子域中定义的地球距离，该距离从上方和下方通过carnot-Carathéodory距离的固定倍数从上方和下方界定。我们表明，这些距离的均匀收敛（在紧凑的集合）中可以按照$γ$ - 连接的几种变异问题来表征。此外，我们研究了内在距离类别，它们的度量衍生物和水平束上定义的子框架指标之间的关系。
This paper is devoted to the study of geodesic distances defined on a subdomain of a given Carnot group, which are bounded both from above and from below by fixed multiples of the Carnot-Carathéodory distance. We show that the uniform convergence (on compact sets) of these distances can be equivalently characterized in terms of $Γ$-convergence of several kinds of variational problems. Moreover, we investigate the relation between the class of intrinsic distances, their metric derivatives and the sub-Finsler convex metrics defined on the horizontal bundle.
