A length comparison theorem for geodesic currents

2022/10/03 by Jenya Sapir, Sapir, Jenya · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2210.00925

openalex publication_date 2022/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We work with the space \mathcal C(S) of geodesic currents on a closed surface S of negative Euler characteristic. By prior work of the author with Sebastian Hensel, each filling geodesic current μ has a unique length-minimizing metric X in Teichmüller space. In this paper, we show that, on so-called thick components of X, the geometries of μ and X are comparable, up to a scalar depending only on μ and the topology of S. We also characterize thick components of the projection using only the length function of μ.

Cited by

• Distinguishing Curve Types and Designer Metrics

Related

• A structure theorem for geodesic currents and length spectrum compactifications
• A projection from filling currents to Teichmüller space
• Length functions on currents and applications to dynamics and counting
• The embedding of the space of negatively curved surfaces in geodesic\n currents
• Critical exponent for geodesic currents