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arXiv · 1809.10090

Convergence of measures on compactifications of locally symmetric spaces

Christopher Daw·Alexander Gorodnik·Emmanuel Ullmo
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Abstract

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $S=\Gamma\backslash G/K$ is compact. More precisely, given a sequence of homogeneous probability measures on $S$, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including $S$ itself). We introduce several tools to study this conjecture and we prove it in a number of cases, including when $G={\rm SL}_3(\mathbb{R})$ and $\Gamma={\rm SL}_3(\mathbb{Z})$.

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Christopher Daw, Alexander Gorodnik, Emmanuel Ullmo. 2018-09-26. Convergence of measures on compactifications of locally symmetric spaces. https://doi.org/10.1007/s00209-020-02558-w

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