Closed geodesics and holonomies for Kleinian manifolds View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2014-10

AUTHORS

Gregory Margulis, Amir Mohammadi, Hee Oh

ABSTRACT

For a rank one Lie group G and a Zariski dense and geometrically finite subgroup Γ of G, we establish the joint equidistribution of closed geodesics and their holonomy classes for the associated locally symmetric space. Our result is given in a quantitative form for geometrically finite real hyperbolic manifolds whose critical exponents are big enough. In the case when G=PSL2(C) , our results imply the equidistribution of eigenvalues of elements of Γ in the complex plane. When Γ is a lattice, the equidistribution of holonomies was proved by Sarnak and Wakayama in 1999 using the Selberg trace formula. More... »

PAGES

1608-1636

References to SciGraph publications

  • 1990-12. Geometrically finite groups, Patterson-Sullivan measures and Ratner's ridigity theorem in INVENTIONES MATHEMATICAE
  • 1984-12. Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups in ACTA MATHEMATICA
  • 1979-12. The density at infinity of a discrete group of hyperbolic motions in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 2004. On Some Aspects of the Theory of Anosov Systems in ON SOME ASPECTS OF THE THEORY OF ANOSOV SYSTEMS
  • 2002-12. On the mixing property for hyperbolic systems in ISRAEL JOURNAL OF MATHEMATICS
  • 1976-12. The limit set of a Fuchsian group in ACTA MATHEMATICA
  • 2010-03. Strong wavefront lemma and counting lattice points in sectors in ISRAEL JOURNAL OF MATHEMATICS
  • 1983-12. The arithmetic and geometry of some hyperbolic three manifolds in ACTA MATHEMATICA
  • 2000-12. Séries de poincaré des groupes géométriquement finis in ISRAEL JOURNAL OF MATHEMATICS
  • 2010-11. Sector Estimates for Hyperbolic Isometries in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 2011-12. Generalization of Selberg’s theorem and affine sieve in ACTA MATHEMATICA
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    URI

    http://scigraph.springernature.com/pub.10.1007/s00039-014-0299-y

    DOI

    http://dx.doi.org/10.1007/s00039-014-0299-y

    DIMENSIONS

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