{"paper":{"title":"Teichm\\\"uller theory for conic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Hartmut Weiss, Rafe Mazzeo","submitted_at":"2015-09-25T07:36:38Z","abstract_excerpt":"In this paper we develop a systematic deformation theory for conic constant curvature metrics on a closed surface when all cone angles are less than $2\\pi$; in particular, we define and study the Teichm\\\"uller space $\\mathcal{T}^{\\mathrm{conic}}_{\\gamma,k}$ of conic constant curvature metrics on a surface of genus $\\gamma$ with $k$ conic points. The methods here are adopted from higher dimensional global analysis, generalizing Tromba's approach to the study of the standard Teichm\\\"uller space $\\mathcal{T}_\\gamma$. The main new ingredient is the theory of elliptic conic operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07608","kind":"arxiv","version":1},"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"}