Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces

Abstract

The paper initiates a systematic study of Moebius structures and Ptolemy spaces. We conjecture that every compact Ptolemy space with circles and many space inversions is Moebius equivalent to the boundary at infinity of a rank one symmetric space of noncompact type. We prove this conjecture for the class of complex hyperbolic spaces as our main result.

77 pages

References in corpus (1)

• Hyperbolicity, CAT(-1)-spaces and the Ptolemy Inequality

Cited by in corpus (5)

• Complex cross--ratios and the Ptolemaean inequality
• Moebius rigidity of invariant metrics in boundaries of symmetric spaces of rank 1
• Cross ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1
• A Flat Strip Theorem for Ptolemaic Spaces
• The Ptolemaean Inequality in the closure of complex hyperbolic plane