Mumford, David2010-02-021971Mumford, David B. 1971. A remark on Mahler's compactness theorem. Proceedings of the American Mathematical Society 28(1): 289-294.0002-9939http://nrs.harvard.edu/urn-3:HUL.InstRepos:3612773We 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.en-USJournal Article2010-02-0210.2307/2037802