Geodesic
Dimensions of $\mathbb R$-Trees and Self-Similar Fractal Spaces of Nonpositive Curvature
Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 3-22

Voir la notice de l'article provenant de la source Math-Net.Ru

We study various dimensions of spaces with nonpositive curvature in the A. D. Alexandrov sense, in particular, of $\mathbb R$-trees. We find some conditions necessary and sufficient for the metric space to be an $\mathbb R$-tree and clarify relations between the topological, Hausdorff, entropy, and rough dimensions. We build the examples of $\mathbb R$-trees and CAT(0)-spaces in which strict inequalities between the topological, Hausdorff, and entropy dimensions hold; we also show that the Hausdorff and entropy dimensions can be arbitrarily large while the topological dimension remains fixed. 
@article{MT_2006_9_2_a0,
     author = {P. D. Andreev and V. N. Berestovskii},
     title = {Dimensions of $\mathbb R${-Trees} and {Self-Similar} {Fractal} {Spaces} of {Nonpositive} {Curvature}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--22},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2006_9_2_a0/}
}
TY  - JOUR
AU  - P. D. Andreev
AU  - V. N. Berestovskii
TI  - Dimensions of $\mathbb R$-Trees and Self-Similar Fractal Spaces of Nonpositive Curvature
JO  - Matematičeskie trudy
PY  - 2006
SP  - 3
EP  - 22
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2006_9_2_a0/
LA  - ru
ID  - MT_2006_9_2_a0
ER  - 
%0 Journal Article
%A P. D. Andreev
%A V. N. Berestovskii
%T Dimensions of $\mathbb R$-Trees and Self-Similar Fractal Spaces of Nonpositive Curvature
%J Matematičeskie trudy
%D 2006
%P 3-22
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2006_9_2_a0/
%G ru
%F MT_2006_9_2_a0
P. D. Andreev; V. N. Berestovskii. Dimensions of $\mathbb R$-Trees and Self-Similar Fractal Spaces of Nonpositive Curvature. Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 3-22. http://geodesic.mathdoc.fr/item/MT_2006_9_2_a0/