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arXiv · 1601.08020

Effective equidistribution of translates of large submanifolds in semisimple homogeneous spaces

Adrián Ubis
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Abstract

Let $G=SL_2(\mathbb R)^d$ and $Γ=Γ_0^d$ with $Γ_0$ a lattice in $SL_2(\mathbb R)$. Let $S$ be any "curved" submanifold of small codimension of a maximal horospherical subgroup of $G$ relative to an $\mathbb R$-diagonalizable element $a$ in the diagonal of $G$. Then for $S$ compact our result can be described by saying that $a^n \text{vol}_S$ converges in an effective way to the volume measure of $G/Γ$ when $n\to \infty$, with $\text{vol}_S$ the volume measure on $S$.

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Adrián Ubis. 2020-07-07. Effective equidistribution of translates of large submanifolds in semisimple homogeneous spaces. https://doi.org/10.1093/imrn%2Frnw179

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