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arXiv · 2501.14067

Horocycles in hyperbolic 3-manifolds with round Sierpi\'nski limit sets

Dongryul M. Kim·Minju Lee
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Abstract

Let M be a geometrically finite hyperbolic 3-manifold whose limit set is a round Sierpi\'nski gasket, i.e. M is geometrically finite and acylindrical with a compact, totally geodesic convex core boundary. In this paper, we classify orbit closures of the 1-dimensional horocycle flow on the frame bundle of M. As a result, the closure of a horocycle in M is a properly immersed submanifold. This extends the work of McMullen-Mohammadi-Oh where M is further assumed to be convex cocompact.

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Dongryul M. Kim, Minju Lee. 2025-01-23. Horocycles in hyperbolic 3-manifolds with round Sierpi\'nski limit sets. https://arxiv.org/abs/2501.14067

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