A Remark on Mahler's Compactness Theorem

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A Remark on Mahler's Compactness Theorem

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Title: A Remark on Mahler's Compactness Theorem
Author: Mumford, David Bryant
Citation: Mumford, David B. 1971. A remark on Mahler's compactness theorem. Proceedings of the American Mathematical Society 28(1): 289-294.
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Abstract: We 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
(a) Γ∩U={e},
(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.
Published Version: doi:10.2307/2037802
Other Sources: http://www.dam.brown.edu/people/mumford/Papers/DigitizedAlgGeomPapers--ForNon-CommercialUse/71b--MahlerComp.pdf
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3612773
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