A Cantor set with hyperbolic complement

2012/05/21 by Juan Souto, Souto, Juan, Matthew Stover +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1205.4668

openalex publication_date 2012/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a Cantor set in S³ whose complement admits a complete hyperbolic metric.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

Related

• About C¹-minimality of the hyperbolic Cantor sets
• Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets
• Extended explanation of Orevkov's paper on proper holomorphic embeddings of complements of Cantor sets in \Bbb C² and a discussion of their measure
• Proper Holomorphic Embeddings of complements of large Cantor sets in \Bbb C²
• Cantor sets with absolutely continuous harmonic measure