A bound for diameter of arithmetic hyperbolic orbifolds

Mikhail Belolipetsky

备注：: 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

英文摘要：

Let $O$ be a closed $n$-dimensional arithmetic (real or complex) hyperbolic orbifold. We show that the diameter of $O$ is bounded above by $$\frac{c_1\log vol(O) + c_2}{h(O)},$$ where $h(O)$ is the Cheeger constant of $O$, $vol(O)$ is its volume, and constants $c_1$, $c_2$ depend only on $n$.

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