Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces

• Autorzy: Sergei Buyalo , Viktor Schroeder
• Języki publikacji: EN

Abstrakty

EN

We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.

Słowa kluczowe

EN

complex hyperbolic spaces; Ptolemy spaces; incidence axioms

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-02-18

zaakceptowano

2015-07-13

online

2015-09-15

Twórcy

autor

Sergei Buyalo

• St. Petersburg Dept. of Steklov Math. Institute RAS, Fontanka 27, 191023 St. Petersburg, Russia, St. Petersburg State University

autor

Viktor Schroeder

• Institut für Mathematik, Universität Zürich, Winterthurer Strasse 190, CH-8057 Zürich, Switzerland

Bibliografia

• [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]
• [3] S. Buyalo, V. Schroeder, Elements of asymptotic geometry, EMS Monographs in Mathematics, 2007, 209 pages.
• [4] R. Chow, Groups quasi-isometric to complex hyperbolic space. Trans. Amer. Math. Soc. 348 (1996), no. 5, 1757–1769.
• [5] T. Foertsch, V. Schroeder, Metric Möbius geometry and a characterization of spheres, Manuscripta Math. 140 (2013), no. 3-4, 613–620. [WoS]
• [6] T. Foertsch, V. Schroeder, Hyperbolicity, CAT(−1)-spaces and Ptolemy inequality, Math. Ann. 350 (2011), no. 2, 339–356. [WoS]
• [7] P. Hitzelberger, A. Lytchak, Spaces with many affine functions, Proc. Amer. Math. Soc. 135 (2007), no. 7, 2263–2271.
• [8] L. Kramer, Two-transitive Lie groups, J. reine angew. Math. 563 (2003), 83–113.
• [9] I. Mineyev, Metric conformal structures and hyperbolic dimension, Conform. Geom. Dyn. 11 (2007), 137–163 (electronic).

Identyfikatory

DOI

10.1515/agms-2015-0015