Geodesic planes in hyperbolic 3-manifolds

By Curtis T. McMullen, A. Mohammadi, H. Oh. Inventiones Mathematicae, 2016

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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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/10409c75bfb2ec6e7bf77d63093230aa93499119