Abstract
Let \({\mathcal {O}}\) be a closed n-dimensional arithmetic (real or complex) hyperbolic orbifold. We show that the diameter of \({\mathcal {O}}\) is bounded above by
where \(h({\mathcal {O}})\) is the Cheeger constant of \({\mathcal {O}}\), \(\mathrm {vol}({\mathcal {O}})\) is its volume, and constants \(c_1\), \(c_2\) depend only on n.
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I would like to thank the referee for careful proofreading of the manuscript and helpful comments. The author is partially supported by CNPq and FAPERJ research grants.
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Belolipetsky, M. A bound for diameter of arithmetic hyperbolic orbifolds. Geom Dedicata 214, 295–302 (2021). https://doi.org/10.1007/s10711-021-00616-z
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DOI: https://doi.org/10.1007/s10711-021-00616-z