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arXiv · 1801.00875

On the growth of the number of totally geodesic surfaces in some hyperbolic $3$-manifolds

Junehyuk Jung
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Abstract

Let $d$ be a positive square-free integer $\equiv 3 \pmod{4}$ such that there is no invariant of the ideal class group $\mathbb{Q}\lbrack \sqrt{-d}\rbrack$ which is divisible by $4$. We prove an asymptotic formula for the number of immersed totally geodesic surfaces in $\Gamma_{-d}\backslash \mathbb{H}^3$ having area less than $X$.

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Junehyuk Jung. 2018-01-03. On the growth of the number of totally geodesic surfaces in some hyperbolic $3$-manifolds. https://arxiv.org/abs/1801.00875

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