Geodesic planes in the convex core of an acylindrical 3-manifold
نویسندگان
چکیده
Let M be a convex cocompact, acylindrical hyperbolic 3-manifold of infinite volume, and let M? denote the interior core M. In this paper we show that any geodesic plane in is either closed or dense. We also only countably many planes are closed. These first rigidity theorems for cocompact 3-manifolds volume depend on topology
منابع مشابه
Geodesic planes in the convex core of an acylindrical 3-manifold
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 inM∗ 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 t...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2022
ISSN: ['1547-7398', '0012-7094']
DOI: https://doi.org/10.1215/00127094-2021-0030