Geodesic
Asymptotic properties of Hilbert geometry
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 3, pp. 327-345 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that the spheres in Hilbert geometry have the same volume growth entropy as those in the Lobachevsky space. Asymptotic estimates for the ratio of the volume of metric ball to the area of the metric sphere in Hilbert geometry are given. Derived estimates agree with the well-known fact in the Lobachevsky space. 
@article{JMAG_2008_4_3_a0,
     author = {A. A. Borisenko and E. A. Olin},
     title = {Asymptotic properties of {Hilbert} geometry},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {327--345},
     year = {2008},
     volume = {4},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2008_4_3_a0/}
}
TY  - JOUR
AU  - A. A. Borisenko
AU  - E. A. Olin
TI  - Asymptotic properties of Hilbert geometry
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2008
SP  - 327
EP  - 345
VL  - 4
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2008_4_3_a0/
LA  - en
ID  - JMAG_2008_4_3_a0
ER  - 
%0 Journal Article
%A A. A. Borisenko
%A E. A. Olin
%T Asymptotic properties of Hilbert geometry
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2008
%P 327-345
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2008_4_3_a0/
%G en
%F JMAG_2008_4_3_a0
A. A. Borisenko; E. A. Olin. Asymptotic properties of Hilbert geometry. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 3, pp. 327-345. http://geodesic.mathdoc.fr/item/JMAG_2008_4_3_a0/

[1] Yu. A. Aminov, The Geometry of Submanifolds, Naukova Dumka, Kyiv, 2002 (Russian) | Zbl

[2] W. Blaschke, Kreis und Kugel, Von Veit, Leipzig, 1916

[3] A. A. Borisenko, An Intrinsic and Extrinsic Geometry of Many-Dimensional Submanifolds, Ekzamen, Moscow, 2003 (Russian)

[4] A. A. Borisenko, “Convex Sets in Hadamard Manifolds”, Diff. Geom. and its Appl., 17 (2002), 111–121 | DOI | MR | Zbl

[5] A. A. Borisenko, E. A. Olin, “Some Comparison Theorems in Finsler–Hadamard Manifolds”, J. Math. Phys., Anal., Geom., 3 (2007), 298–312 | MR | Zbl

[6] A. A. Borisenko, E. Gallego, A. Reventos, “Relation Between Area and Volume for Convex Sets in Hadamard Manifolds”, Diff. Geom. and its Appl., 14 (2001), 267–280 | DOI | MR | Zbl

[7] A. A. Borisenko, V. Miquel, “Comparison Theorem on Convex Hypersurfaces in Hadamard Manifolds”, Ann. Global Anal. and Geom., 21 (2002), 191–202 | DOI | MR | Zbl

[8] Yu. D. Burago, V. A. Zalgaller, An Introduction to Riemann Geometry, Nauka, Moscow, 1994 (Russian) | MR | Zbl

[9] H. Busemann, “Intrinsic Area”, Ann. Math.(2), 48 (1947), 234–267 | DOI | MR

[10] H. Busemann, The Geometry of Geodesics, Acad. Press, New York, 1955 | MR | Zbl

[11] H. Busemann, K. Kelly, Projective Geometry and Projective Metrics, Acad. Press, New York, 1953 | MR | Zbl

[12] B. Colbois, P. Verovic, “Rigidity of Hilbert Metrics”, Bull. Austral. Math. Soc., 65 (2002), 23–34 | DOI | MR | Zbl

[13] B. Colbois, P. Verovic, “Hilbert Geometries for Strictly Convex Domains”, Geom. Dedicata, 105 (2004), 29–42 | DOI | MR | Zbl

[14] D. Egloff, “Uniform Finsler Hadamard Manifolds”, Ann. de l'Institut Henri Poincare, 66:3 (1997), 323–357 | MR | Zbl

[15] A. V. Pogorelov, Differential Geometry, Nauka, Moscow, 1974 (Russian) | MR

[16] Z. Shen, Lectures on Finsler Geometry, World Sci. Publ. Co, Indiana Univ., Purdue Univ., Indianapolis, 2001 | MR