Geodesic
$cc$-Homogeneous Cone Condition and $cc$-Balls on Heizenberg Groups
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 4, pp. 8-20

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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. 
@article{VNGU_2011_11_4_a1,
     author = {A. V. Belykh and A. V. Greshnov},
     title = {$cc${-Homogeneous} {Cone} {Condition} and $cc${-Balls} on {Heizenberg} {Groups}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {8--20},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_4_a1/}
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A. V. Belykh; A. V. Greshnov. $cc$-Homogeneous Cone Condition and $cc$-Balls on Heizenberg Groups. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 4, pp. 8-20. http://geodesic.mathdoc.fr/item/VNGU_2011_11_4_a1/