Carnot–Carathéodory Homogeneous Cone Condition and Carnot–Carathéodory Balls in Heisenberg Groups

Carnot–Carathéodory Homogeneous Cone Condition and Carnot–Carathéodory Balls in Heisenberg Groups

We study properties of extremals of the variational problem about the shortest paths in the Carnot–Carathéodory metric on Heisenberg groups. We prove that the Carnot–Carathéodory balls in Heisenberg groups satisfy the Carnot–Carathéodory homogeneous cone condition. Bibliography: 17 titles.

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2013-12, Vol.195 (6), p.779-790
Hauptverfasser: Belykh, A. V., Greshnov, A. V.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:We study properties of extremals of the variational problem about the shortest paths in the Carnot–Carathéodory metric on Heisenberg groups. We prove that the Carnot–Carathéodory balls in Heisenberg groups satisfy the Carnot–Carathéodory homogeneous cone condition. Bibliography: 17 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-013-1617-x