Convergence of measures on compactifications of locally symmetric spacesDaw, C., Gorodnik, A. and Ullmo, E. (2020) Convergence of measures on compactifications of locally symmetric spaces. Mathematische Zeitschrift. ISSN 0025-5874
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1007/s00209-020-02558-w Abstract/SummaryWe conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space S=Γ∖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=SL3(R) and Γ=SL3(Z).
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