{"paper":{"title":"Geodesics Currents and Counting Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Juan Souto, Kasra Rafi","submitted_at":"2017-09-20T12:31:02Z","abstract_excerpt":"For every positive, continuous and homogeneous function $f$ on the space of currents on a compact surface $\\overline{\\Sigma}$, and for every compactly supported filling current $\\alpha$, we compute as $L \\to \\infty$, the number of mapping classes $\\phi$ so that $f(\\phi(\\alpha))\\leq L$. As an application, when the surface in question is closed, we prove a lattice counting theorem for Teichm\\\"uller space equipped with the Thurston metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06834","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}