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arXiv · 2310.00169

Margulis' Inequality for translates of horospherical orbits and applications to equidistribution

Asaf Katz
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Abstract

In this paper we develope a quantitative non-divergence theorem for translates of horospherical orbits, using the technique of Margulis' inequality as developed by Eskin-Margulis-Mozes and Eskin-Margulis. As we use the Margulis' inequality, our results do not depend on the spectral gap of the action. As an application of our techniques, we show that given a horospherical flow over the space of lattices, the horospherical orbit of every lattice defined over a number field, not contained in a proper rational parabolic subgroup is equidistributed with an effective rate.

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Asaf Katz. 2023-09-29. Margulis' Inequality for translates of horospherical orbits and applications to equidistribution. https://arxiv.org/abs/2310.00169

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