Geodesic
On the geometry of similarly homogeneous $\mathbb{R}$-trees
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2020), pp. 3-15 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the geometry of the locally complete similarly homogeneous $\mathbb R$-trees. We prove the existence theorem for the class of vertical $\mathbb R$-trees which are not strongly vertical introduced earlier. The analogous method is applicable to other classes of locally complete similarly homogeneous $\mathbb R$-trees.
Keywords: similarly homogenous space, vertical $\mathbb R$-tree, saw-like function. 
@article{IVM_2020_4_a0,
     author = {P. D. Andreev and A. I. Bulygin},
     title = {On the geometry of similarly homogeneous $\mathbb{R}$-trees},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--15},
     year = {2020},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_4_a0/}
}
TY  - JOUR
AU  - P. D. Andreev
AU  - A. I. Bulygin
TI  - On the geometry of similarly homogeneous $\mathbb{R}$-trees
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 3
EP  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_4_a0/
LA  - ru
ID  - IVM_2020_4_a0
ER  - 
%0 Journal Article
%A P. D. Andreev
%A A. I. Bulygin
%T On the geometry of similarly homogeneous $\mathbb{R}$-trees
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 3-15
%N 4
%U http://geodesic.mathdoc.fr/item/IVM_2020_4_a0/
%G ru
%F IVM_2020_4_a0
P. D. Andreev; A. I. Bulygin. On the geometry of similarly homogeneous $\mathbb{R}$-trees. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2020), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2020_4_a0/

[1] Berestovskii V.N., “Podobno odnorodnye lokalno polnye prostrantva s vnutrennei metrikoi”, Izv. vuzov. Matem., 2004, no. 11, 3–22 | Zbl

[2] Gundyrev I.A., Podobno odnorodnye prostranstva s vnutrennei metrikoi, Diss. na soiskanie uchenoi stepeni kand. fiz.-matem. nauk, Omsk, 2015 | Zbl

[3] Andreev P.D., “Polulineinye metricheskie polureshetki na $\mathbb R$-derevyakh”, Izv. vuzov. Matem., 2007, no. 6, 3–13 | Zbl

[4] Andreev P.D., Bulygin A.I., “On the vertical similarly homogeneous $\mathbb R$-trees”, Lobachevskii J. Math., 40:2 (2019), 127–139 | DOI | MR | Zbl

[5] Bestvina M., “$\mathbb R$-trees in topology, geometry and group theory”, Handbook of geometric topology, eds. R.J. Daverman, R.B. Sher, Elsevier Sci., North-Holland, Amsterdam–London–New York, 2002, 55–91 | MR | Zbl

[6] Berestovski\v{i} V.N., Plaut C., “Covering $\mathbb R$-trees, $\mathbb R$-free groups, and dendrites”, Adv. Math., 224:5 (2010), 1765–1783 | DOI | MR | Zbl

[7] Andreev P.D., Berestovskii V.N., “Razmernosti $\mathbb R$-derevev i samopodobnye fraktalnye prostranstva nepolozhitelnoi krivizny”, Matem. tr., 9:2 (2006), 3–22 | Zbl

[8] Birkgof G., Teoriya reshetok, 3-e izd., Nauka, M., 1984 | MR