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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 938–948 (Mi semr1104)  

Real, complex and functional analysis

Hyperspaces that satisfy $cc$-homogeneous cone condition on canonical Heisenberg and Engel groups

A. V. Greshnovab

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

Abstract: We get a new proof that hyperspace $\{(x,y,t)\mid t>0\}$ of canonical Heisenberg group $\mathbb {H}^1$ satisfies inner and outer continuously deformable $cc$-homogeneous cone conditions and $cc$-uniformity condition. By means of that we prove that hyperspace $\{(x,y,t,z)\mid t>0\}$ of canonical Engel group $\mathbb {E}_{\alpha,\beta}$ satisfies inner and outer continuously deformable $cc$-homogeneous cone conditions.

Keywords: Carnot–Carathéodory metric, $cc$-homogeneous cone, Heisenberg group, Engel group, inner cone, outer cone, $cc$-uniform domain, hyperspace.

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


DOI: https://doi.org/10.33048/semi.2019.16.062

Full text: PDF file (187 kB)
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Bibliographic databases:

UDC: 517.518
MSC: 43A80
Received May 23, 2019, published June 28, 2019

Citation: A. V. Greshnov, “Hyperspaces that satisfy $cc$-homogeneous cone condition on canonical Heisenberg and Engel groups”, Sib. Èlektron. Mat. Izv., 16 (2019), 938–948

Citation in format AMSBIB
\Bibitem{Gre19}
\by A.~V.~Greshnov
\paper Hyperspaces that satisfy $cc$-homogeneous cone condition on canonical Heisenberg and Engel groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 938--948
\mathnet{http://mi.mathnet.ru/semr1104}
\crossref{https://doi.org/10.33048/semi.2019.16.062}


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