2009/01/24 by Guowu Yao, Yao, Guowu
Mathematics · #30C62 #30C75 #32G15 #Analytic and geometric function theory #Binary number #Complex Variables (math.CV) #Conjecture #Equivalence (formal languages) #FOS: Mathematics #Geodesic #Infinitesimal #Mathematical analysis #Mathematics #Metric (unit) #Pure mathematics #Riemann sphere #Riemann surface #Teichmüller space #Type (biology) #Unit (ring theory) #Unit disk #math.CV #msc:30C62 #msc:30C75 #msc:32G15
paper · pdf · doi:10.48550/arxiv.0901.3822
10 pages(to appear after modified)
openalex publication_date 2009/01/24 · arxiv created 2009/02/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let S be a Riemann surface of analytic finite type or the unit disk in the complex plane. Let [μ] denote the Teichmüller equivalence classes of Beltrami differentials μ. We apply the Fundamental Inequalities to obtain a binary infinitesimal form of Teichmüller metric. Using this form, we define "angle" between two geodesics originating from a point and conjecture that the sum of the angles of a triangle in T(S) should be less than π if S is of analytic finite type. As a consequence, the well-known necessary condition for two geodesics coinciding is derived immediately.