{"paper":{"title":"Deforming hyperbolic hexagons with applications to the arc and the Thurston metrics on Teichm{\\\"u}ller spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA), Sumio Yamada","submitted_at":"2015-12-09T07:46:33Z","abstract_excerpt":"For each right-angled hexagon in the hyperbolic plane, we construct a one-parameter family of right-angled hexagons with a Lipschitz map between any two elements in this family,  realizing the smallest Lipschitz constant in the homotopy class of this map relative to the boundary.  As a consequence of this construction, we exhibit new geodesics for the arc metric on the Teichm{\\\"u}ller space of an arbitrary surface of negative Euler characteristic with nonempty  boundary. We also obtain new geodesics for Thurston's metric on Teichm{\\\"u}ller spaces of hyperbolic surfaces without boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02776","kind":"arxiv","version":3},"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"}