A better proof of the Goldman-Parker conjecture.
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Schwartz, Richard Evan (2005)
Geometry & Topology
Floyd L. Williams (1992)
Manuscripta mathematica
Anna Wienhard (2003/2004)
Séminaire de théorie spectrale et géométrie
M. Kanai (1996)
Geometric and functional analysis
M.S. RAGHUNATHAN (1967/1968)
Inventiones mathematicae
Claudio Nebbia (1989)
Monatshefte für Mathematik
Nelo, D. Allan (1973)
Revista colombiana de matematicas
Tadeusz Pytlik (1979)
Colloquium Mathematicae
Bachir Bekka, Yves Cornulier (2010)
Colloquium Mathematicae
Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation of G on L²(G/H) has a spectral gap, that is, the restriction of to the orthogonal complement of the constants in L²(G/H) does not have almost invariant vectors. This answers a question of G. Margulis. We give an application to the spectral geometry of locally symmetric Riemannian spaces of infinite volume.
Gero Fendler (1990)
Colloquium Mathematicae
M. KUGA, I. SATAKE (1967)
Mathematische Annalen
Frédéric Paulin (1995/1996)
Séminaire Bourbaki
Armand Borel, Gopal Prasad (1990)
Publications Mathématiques de l'IHÉS
Mikhail Belolipetsky (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
There are errors in the proof of uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.
A. Iozzi, A. Nevo (1996)
Geometric and functional analysis
Patrick Ghanaat (1989)
Journal für die reine und angewandte Mathematik
Roberto J. Miatello (1983)
Mathematische Zeitschrift
Martin Moskowitz (2005)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
Anish Ghosh, Robert Royals (2015)
Acta Arithmetica
We prove a version of the Khinchin-Groshev theorem in Diophantine approximation for quadratic extensions of function fields in positive characteristic.
Hisashi Kasuya (2016)
Complex Manifolds
For a simply connected solvable Lie group G with a lattice Γ, the author constructed an explicit finite-dimensional differential graded algebra A*Γ which computes the complex valued de Rham cohomology H*(Γ, C) of the solvmanifold Γ. In this note, we give a quick introduction to the construction of such A*Γ including a simple proof of H*(A*Γ) ≅ H*(Γ, C).
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