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arXiv · 1802.03853

Geodesic planes in the convex core of an acylindrical 3-manifold

Curtis T. McMullen·Amir Mohammadi·Hee Oh
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Abstract

Let $M$ be a convex cocompact acylindrical hyperbolic 3-manifold of infinite volume, and let $M^*$ denote the interior of the convex core of $M$. In this paper we show that any geodesic plane in $M^*$ is either closed or dense. We also show that only countably many planes are closed. These are the first rigidity theorems for planes in convex cocompact 3-manifolds of infinite volume that depend only on the topology of M.

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Curtis T. McMullen, Amir Mohammadi, Hee Oh. 2018-02-12. Geodesic planes in the convex core of an acylindrical 3-manifold. https://arxiv.org/abs/1802.03853

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