Balls in complex hyperbolic manifolds

2012/03/16 by Baohua Xie, Xie, Baohua, Jieyan Wang +4
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications #math.DG

paper · pdf · doi:10.48550/arxiv.1203.3610

8 pages

openalex publication_date 2012/03/16 · arxiv created 2013/04/07 · arxiv updated 2013/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we get an explicit lower bound for the radius of a Bergman ball contained in the Dirichlet fundamental polyhedron of a torsion-free discrete group G⊂ PU(n,1) acting on complex hyperbolic space. Consequently the volume of all complex hyperbolic n-manifolds is bounded below by the volume of this ball.

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