The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume

Simon T. Drewitz; Ruth Kellerhals

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arXiv · 2106.12279

The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume

Simon T. Drewitz·Ruth Kellerhals

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Abstract

We show that the 1-cusped quotient of the hyperbolic space $\mathbb{H}^3$ by the tetrahedral Coxeter group $\Gamma_*=[5,3,6]$ has minimal volume among all non-arithmetic cusped hyperbolic 3-orbifolds, and as such it is uniquely determined. Furthermore, the lattice $\Gamma_*$ is incommensurable to any Gromov-Piatetski-Shapiro type lattice. Our methods have their origin in the work of C. Adams. We extend considerably this approach via the geometry of the underlying horoball configuration induced by a cusp.

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Simon T. Drewitz, Ruth Kellerhals. 2021-06-23. The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume. https://arxiv.org/abs/2106.12279

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