Non-divergence of translates of certain algebraic measures

Alex Eskin*, Shahar Mozes, Nimish Shah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

Let G and H ⊂ G be connected reductive real algebraic groups defined over ℚ, and admitting no nontrivial ℚ-characters. Let Γ ⊂ G(ℚ) be an arithmetic lattice in G, and π : G → Γ\G be the natural quotient map. Let μH denote the H-invariant probability measure on the closed orbit π(H). Suppose that π(Z(H)) is compact, where Z(H) denotes the centralizer of H in G. We prove that the set {μH ·g : g ∈ G} of translated measures is relatively compact in the space of all Borel probability measures on Γ\G, where μH ·g(E) = μH(Eg-1) for all Borel sets E ⊂ Γ\G.

Original languageAmerican English
Pages (from-to)48-80
Number of pages33
JournalGeometric and Functional Analysis
Volume7
Issue number1
DOIs
StatePublished - 1997

Bibliographical note

Funding Information:
The second author is sponsored in part by the Edmund Landau Center for research in Mathematical Analysis supported by the Minerva Foundation (Germany), and by the Israel Academy of Sciences

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