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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2011, Volume 11, Issue 4, Pages 8–20 (Mi vngu96)  

This article is cited in 1 scientific paper (total in 1 paper)

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

A. V. Belykha, A. V. Greshnovba

a 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.

Full text: PDF file (250 kB)
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English version:
Journal of Mathematical Sciences, 2013, 195:6, 779–790

UDC: 517.548.2+517.972.6+517.982.22
Received: 27.08.2010

Citation: A. V. Belykh, A. V. Greshnov, “$cc$-Homogeneous Cone Condition and $cc$-Balls on Heizenberg Groups”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:4 (2011), 8–20; J. Math. Sci., 195:6 (2013), 779–790

Citation in format AMSBIB
\Bibitem{BelGre11}
\by A.~V.~Belykh, A.~V.~Greshnov
\paper $cc$-Homogeneous Cone Condition and $cc$-Balls on Heizenberg Groups
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2011
\vol 11
\issue 4
\pages 8--20
\mathnet{http://mi.mathnet.ru/vngu96}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 195
\issue 6
\pages 779--790
\crossref{https://doi.org/10.1007/s10958-013-1617-x}


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    This publication is cited in the following articles:
    1. A. V. Greshnov, “The geometry of $cc$-balls and the constants in the Ball-Box theorem on Heisenberg group algebras”, Siberian Math. J., 55:5 (2014), 849–865  mathnet  crossref  mathscinet  isi
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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