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Inventiones mathematicae

, Volume 209, Issue 2, pp 425–461 | Cite as

Geodesic planes in hyperbolic 3-manifolds

  • Curtis T. McMullen
  • Amir Mohammadi
  • Hee Oh
Article

Abstract

This paper initiates the study of rigidity for immersed, totally geodesic planes in hyperbolic 3-manifolds M of infinite volume. In the case of an acylindrical 3-manifold whose convex core has totally geodesic boundary, we show that the closure of any immersed geodesic plane is a properly immersed submanifold of M. On the other hand, we show that rigidity fails for quasifuchsian manifolds.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Curtis T. McMullen
    • 1
  • Amir Mohammadi
    • 2
  • Hee Oh
    • 3
    • 4
  1. 1.Mathematics DepartmentHarvard UniversityCambridgeUSA
  2. 2.Mathematics DepartmentUniversity of CaliforniaSan DiegoUSA
  3. 3.Mathematics DepartmentYale UniversityNew HavenUSA
  4. 4.Korea Institute for Advanced StudySeoulKorea

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