Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$

Elon Lindenstrauss; Amir Mohammadi

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arXiv · 2112.14562

Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$

Elon Lindenstrauss·Amir Mohammadi

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Abstract

We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

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BibTeX RIS

Elon Lindenstrauss, Amir Mohammadi. 2021-12-29. Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$. https://arxiv.org/abs/2112.14562

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