Geodesic Currents and Counting Problems

Geodesic Currents and Counting Problems

For every positive, continuous and homogeneous function f on the space of currents on a compact surface Σ ¯ , and for every compactly supported filling current α , we compute as L → ∞ , the number of mapping classes ϕ so that f ( ϕ ( α ) ) ≤ L . As an application, when the surface in question is clo...

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Veröffentlicht in:Geometric and functional analysis 2019-06, Vol.29 (3), p.871-889
Hauptverfasser: Rafi, Kasra, Souto, Juan
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Sprache:eng
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Analysis
Continuity (mathematics)
Mapping
Mathematics
Mathematics and Statistics
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description For every positive, continuous and homogeneous function f on the space of currents on a compact surface Σ ¯ , and for every compactly supported filling current α , we compute as L → ∞ , the number of mapping classes ϕ so that f ( ϕ ( α ) ) ≤ L . As an application, when the surface in question is closed, we prove a lattice counting theorem for Teichmüller space equipped with the Thurston metric.
doi_str_mv 10.1007/s00039-019-00502-7
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subjects Analysis
Continuity (mathematics)
Mapping
Mathematics
Mathematics and Statistics
title Geodesic Currents and Counting Problems
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