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arXiv · 2312.07719

Topology of horocycles on geometrically finite nonpositively curved surfaces

Sergi Burniol Clotet
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Abstract

We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow.

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Sergi Burniol Clotet. 2023-12-12. Topology of horocycles on geometrically finite nonpositively curved surfaces. https://arxiv.org/abs/2312.07719

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