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- W2023131335 abstract "Let ρ n (V) be the number of complete hyperbolic manifolds of dimension n with volume less than V . Burger et al [Geom. Funct. Anal. 12(6) (2002), 1161–1173.] showed that when n ≥ 4 there exist a, b > 0 depending on the dimension such that aV log V ≤ log ρ n (V) ≤ bV log V, for V ≫ 0. In this note, we use their methods to bound the number of hyperbolic manifolds with diameter less than d and show that the number grows double-exponentially with volume. Additionally, this bound holds in dimension 3." @default.
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- W2023131335 date "2005-11-26" @default.
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- W2023131335 title "Counting Hyperbolic Manifolds with Bounded Diameter" @default.
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- W2023131335 doi "https://doi.org/10.1007/s10711-005-9000-9" @default.
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