Geodesic
Geometry of Ideal Boundaries of Geodesic Spaces with Nonpositive Curvature in the Sense of Busemann
Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 16-28.

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

We establish relations between different approaches to the ideal closure of a geodesic metric space with nonpositive curvature in the sense of Busemann. We construct the counterexample showing that the Busemann ideal closure can differ from the geodesic closure. 
@article{MT_2007_10_1_a1,
     author = {P. D. Andreev},
     title = {Geometry of {Ideal} {Boundaries} of {Geodesic} {Spaces} with {Nonpositive} {Curvature} in the {Sense} of {Busemann}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {16--28},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2007_10_1_a1/}
}
TY  - JOUR
AU  - P. D. Andreev
TI  - Geometry of Ideal Boundaries of Geodesic Spaces with Nonpositive Curvature in the Sense of Busemann
JO  - Matematičeskie trudy
PY  - 2007
SP  - 16
EP  - 28
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2007_10_1_a1/
LA  - ru
ID  - MT_2007_10_1_a1
ER  - 
%0 Journal Article
%A P. D. Andreev
%T Geometry of Ideal Boundaries of Geodesic Spaces with Nonpositive Curvature in the Sense of Busemann
%J Matematičeskie trudy
%D 2007
%P 16-28
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2007_10_1_a1/
%G ru
%F MT_2007_10_1_a1
P. D. Andreev. Geometry of Ideal Boundaries of Geodesic Spaces with Nonpositive Curvature in the Sense of Busemann. Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 16-28. http://geodesic.mathdoc.fr/item/MT_2007_10_1_a1/

[1] Buzeman G., Geometriya geodezicheskikh, Fizmatgiz, M., 1955

[2] Burago D. Yu., Burago Yu. D., Ivanov S. V., Kurs metricheskoi geometrii, Institut kompyuternykh issledovanii, M.; Izhevsk, 2004

[3] Kuratovskii K., Topologiya, t. 1, Mir, M., 1966 | MR

[4] Ballmann W., “The Martin boundary of certain Hadamard manifolds”, Proc. on Analysis and Geometry, ed. Vodop'yanov S. K., Sobolev Institute Press, Novosibirsk, 2000, 36–46 | MR | Zbl

[5] Ballmann W., Gromov M., and Schroeder V., Manifolds of Nonpositive Curvature, Birkhäuser, Boston; Basel; Schtuttgart, 1985 | MR | Zbl

[6] Bowditch B. H., “Minkowskian subspaces of nonpositively curved metric spaces”, Bull. London Math. Soc., 27:6 (1995), 575–584 | DOI | MR | Zbl

[7] Bridson M. R. and Haefliger A., Metric Spaces of Nonpositive Curvature, Die Grundlehren der Mathematischen Wissenschaften, 319, Springer-Verlag, Berlin, 1999 | MR | Zbl

[8] Busemann H., “Spaces with nonpositive curvature”, Acta Math., 80 (1948), 259–310 | DOI | MR

[9] Busemann H. and Phadke B. B., Spaces with Distinguished Geodesics, Marsel Dekker Inc., New-York; Basel, 1987 | MR | Zbl

[10] Eberlein P. and O'Neill B., “Visibility manifolds”, Pacific J. Math., 46 (1973), 45–109 | MR | Zbl

[11] Gromov M., “Hyperbolic groups”, Essays in Group Theory, Math. Sci. Res. Inst. Publ., 8, ed. Gersten S. M., Springer-Verlag, Berlin, 1987, 75–263 | MR

[12] Hosaka T., “Limit sets of geometrically finite groups acting on Busemann spaces”, Topology Appl., 122:3 (2002), 565–580 | DOI | MR | Zbl

[13] Hotchkiss Ph. K., “The boundary of Busemann space”, Proc. Amer. Math. Soc., 125:7 (1997), 1903–1912 | DOI | MR | Zbl

[14] Kapovich I. and Benakli N., “Boundaries of hyperbolic groups: Combinatorial and geometric group theory”, Contemp. Math., 296 (2004), 39–94 | MR

[15] Martin R. S., “Minimal positive harmonic functions”, Trans. Amer. Math. Soc., 49 (1941), 137–172 | DOI | MR | Zbl

[16] Rieffel M., “Group $C^*$-algebras as compact quantum metric spaces”, Doc. Math., 7 (2002), 605–651 | MR | Zbl

[17] Rinow W., Die Innere Geometrie der Metrischen Raume, Die Grundlehren der Mathematischen Wissenschaften, 105, Springer-Verlag, Berlin; Gottingen; Heidelberg, 1961 | MR | Zbl

[18] Webster C. and Winchester A., Boundaries of Hyperbolic Metric Spaces, Preprint: , 2003 arXiv: math.MG/0310101 | MR