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Coxeter polytopes and Benjamini--Schramm convergence (2209.03002v1)
Published 7 Sep 2022 in math.GT
Abstract: We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work with M. Fraczyk and S. Hurtado. We also study in more depth the case of polygons in the hyperbolic plane.
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