The Stable Neighborhood Theorem and Lengths of Closed Geodesics

DOI10.2307/2159845zbMath0779.30030OpenAlexW4253583125MaRDI QIDQ3141306

Ara Basmajian

Publication date: 28 November 1993

Full work available at URL: https://doi.org/10.2307/2159845

zbMATH Keywords

closed geodesichyperbolic surfaceself-intersection numbercollar lemma

Mathematics Subject Classification ID

Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (7)

Short closed geodesics on cusped hyperbolic surfaces ⋮ Generalizing the hyperbolic collar lemma ⋮ Length minima for an infinite family of filling closed curves on a one-holed torus ⋮ The shortest non-simple closed geodesics on hyperbolic surfaces ⋮ Prising apart geodesics by length in hyperbolic manifolds ⋮ A property of closed geodesics on hyperbolic surfaces ⋮ Short closed geodesics with self-intersections

Cites Work

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• The lengths of the closed geodesics on a Riemann surface with self- intersections.
• On Marden's universal constant of Fuchsian groups. II
• Traces, lengths, and simplicity for loops on surfaces
• The real analytic theory of Teichmüller space
• On Marden's universal constant of Fuchsian groups
• A compactness theorem for Fuchsian groups of the second kind
• Cylinders in Riemann surfaces
• The collar theorem and examples
• An algorithm for 2-generator Fuchsian groups
• Comparison of hyperbolic and extremal lengths
• Constructing pairs of pants
• A Proof of the Collar Lemma

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