Geodesic planes in hyperbolic 3-manifolds | Zendy

Curtis T. McMullen | Zendy; Amir Mohammadi | Zendy; Hee Oh | Zendy

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Geodesic planes in hyperbolic 3-manifolds

Author(s) -

Curtis T. McMullen,

Amir Mohammadi,

Hee Oh

Publication year - 2016

Publication title -

inventiones mathematicae

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.536

H-Index - 125

eISSN - 1432-1297

pISSN - 0020-9910

DOI - 10.1007/s00222-016-0711-3

Subject(s) - mathematics , geodesic , submanifold , rigidity (electromagnetism) , totally geodesic , regular polygon , hyperbolic manifold , pure mathematics , mathematical analysis , geometry , physics , hyperbolic function , quantum mechanics

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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