We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
@article{bwmeta1.element.doi-10_1515_agms-2015-0015,
author = {Sergei Buyalo and Viktor Schroeder},
title = {Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1344.53026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0015}
}
Sergei Buyalo; Viktor Schroeder. Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0015/
[1] S. Buyalo, V. Schroeder, Möbius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces, arXiv:1012.1699, 2010.
[2] S. Buyalo, V. Schroeder, Möbius characterization of the boundary at infinity of rank one symmetric spaces, Geometriae Dedicata, 172, (2014), no.1, 1-45. [WoS] | Zbl 06357997
[3] S. Buyalo, V. Schroeder, Elements of asymptotic geometry, EMS Monographs in Mathematics, 2007, 209 pages. | Zbl 1125.53036
[4] R. Chow, Groups quasi-isometric to complex hyperbolic space. Trans. Amer. Math. Soc. 348 (1996), no. 5, 1757–1769. | Zbl 0867.20033
[5] T. Foertsch, V. Schroeder, Metric Möbius geometry and a characterization of spheres, Manuscripta Math. 140 (2013), no. 3-4, 613–620. [WoS] | Zbl 1270.51016
[6] T. Foertsch, V. Schroeder, Hyperbolicity, CAT(−1)-spaces and Ptolemy inequality, Math. Ann. 350 (2011), no. 2, 339–356. [WoS] | Zbl 1219.53042
[7] P. Hitzelberger, A. Lytchak, Spaces with many affine functions, Proc. Amer. Math. Soc. 135 (2007), no. 7, 2263–2271. | Zbl 1128.53021
[8] L. Kramer, Two-transitive Lie groups, J. reine angew. Math. 563 (2003), 83–113. | Zbl 1044.22014
[9] I. Mineyev, Metric conformal structures and hyperbolic dimension, Conform. Geom. Dyn. 11 (2007), 137–163 (electronic). | Zbl 1165.20035