This article is cited in 1 paper

$cc$-Homogeneous Cone Condition and $cc$-Balls on Heizenberg Groups

A. V. Belykh^a, A. V. Greshnov<sup>ba

a</sup> Novosibirsk State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We studied properties of extremals of variational problem about the shortest paths of Carnot–Carathéodory metric (the $cc$-shortest paths) on Heizenberg groups. Using the establishing results we proved that $cc$-balls are satisfying the $cc$-homogeneous cone property.

Keywords: extremals, shortest path, Carnot–Carathéodory metric, Pontryagin maximum principle, Heizenberg groups.

UDC: 517.548.2+517.972.6+517.982.22

Received: 27.08.2010

 English version: Journal of Mathematical Sciences, 2013, 195:6, 779–790