A Remark on Mahler's Compactness Theorem
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CitationMumford, David B. 1971. A remark on Mahler's compactness theorem. Proceedings of the American Mathematical Society 28(1): 289-294.
AbstractWe prove that if G is a semisimple Lie group without compact factors, then for all open sets U⊂G containing the unipotent elements of G and for all C>0, the set of discrete subgroups Γ⊂G such that
(b) G/Γ compact and measure (G/Γ)≤C,
is compact. As an application, for any genus g and ∈>0, the set of compact Riemann surfactes fo genus g all of whose closed geodesics in the Poincare metric have length ≥∈, is itself compact.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:3612773
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