A bound for diameter of arithmetic hyperbolic orbifolds

2020/01/16 by Mikhail Belolipetsky, Belolipetsky, Mikhail
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #math.GT #math.MG

paper · pdf · doi:10.48550/arxiv.2001.07520

9 pages, final version, to appear in Geom. Dedicata. The paper uses and extends to the complex hyperbolic orbifolds some results of arXiv:math/0612132 and arXiv:1811.05280

arxiv created 2021/02/24 · arxiv updated 2021/02/25

Abstract

Let O be a closed n-dimensional arithmetic (real or complex) hyperbolic orbifold. We show that the diameter of O is bounded above by (c₁log vol(O) + c₂)/(h(O)), where h(O) is the Cheeger constant of O, vol(O) is its volume, and constants c₁, c₂ depend only on n.

Citations

• Finiteness of arithmetic hyperbolic reflection groups
• Thickness of skeletons of arithmetic hyperbolic orbifolds

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