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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1182–1197 (Mi semr987)  

Real, complex and functional analysis

Uniformity of $cc$-balls on some class of 2-step Carnot groups

A. V. Greshnovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, ul. Pirogova, 1, 630090, Novosibirsk, Russia

Abstract: For some class of 2-step Carnot groups $\Bbb H_{\alpha_1,…,\alpha_n}^1$ that includes Heizenberg groups we proved that Carnot-Carathéodory balls ($cc$-balls) of these groups are uniform domains. We studied the geometry of the set of points of $\Bbb H_{\alpha_1,…,\alpha_n}^1$ joined with identity element of $\Bbb H_{\alpha_1,…,\alpha_n}^1$ more than one Carnot-Carathéodory $cc$- shortest path.

Keywords: Carnot–Carathéodory shortest path, cc-ball, extremal, uniform domain, Heisenberg groups.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.3087.2017/4.6


DOI: https://doi.org/10.17377/semi.2018.15.096

Full text: PDF file (223 kB)
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Document Type: Article
UDC: 517.54, 517.97
MSC: 30C65, 30G35, 53C17
Received August 20, 2018, published October 16, 2018

Citation: A. V. Greshnov, “Uniformity of $cc$-balls on some class of 2-step Carnot groups”, Sib. Èlektron. Mat. Izv., 15 (2018), 1182–1197

Citation in format AMSBIB
\Bibitem{Gre18}
\by A.~V.~Greshnov
\paper Uniformity of $cc$-balls on some class of 2-step Carnot groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1182--1197
\mathnet{http://mi.mathnet.ru/semr987}
\crossref{https://doi.org/10.17377/semi.2018.15.096}


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