Geodesic
Hyperspaces that satisfy $cc$-homogeneous cone condition on canonical Heisenberg and Engel groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 938-948

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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, hyperspace.
Mots-clés : outer cone, $cc$-uniform domain 
@article{SEMR_2019_16_a136,
     author = {A. V. Greshnov},
     title = {Hyperspaces that satisfy $cc$-homogeneous cone condition on canonical {Heisenberg} and {Engel} groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {938--948},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a136/}
}
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A. V. Greshnov. Hyperspaces that satisfy $cc$-homogeneous cone condition on canonical Heisenberg and Engel groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 938-948. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a136/