# Geodesic planes in hyperbolic 3-manifolds

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## 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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