2018/11/13 by Hannah Alpert, Mikhail Belolipetsky, Alpert, Hannah +1 · 1 citation
Mathematics · #53C23 #57R18 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C23 #msc:57R18
paper · pdf · doi:10.48550/arxiv.1811.05280
15 pages, filled a gap in the proof of Theorem 2, final version, to appear in J. of Topology & Analysis
arxiv created 2021/03/04 · arxiv updated 2021/03/05
We show that closed arithmetic hyperbolic n-dimensional orbifolds with larger and larger volumes give rise to triangulations of the underlying spaces whose 1-skeletons are harder and harder to embed nicely in Euclidean space. To show this we generalize an inequality of Gromov and Guth to hyperbolic n-orbifolds and find nearly optimal geodesic triangulations of arithmetic hyperbolic n-orbifolds.