Díaz Sánchez, RaquelUshijima, Akira2023-06-202023-06-2020090146-4124https://hdl.handle.net/20.500.14352/50026In this paper we give necessary and sufficient conditions on three orientation-preserving hyperbolic isometries T1,T2,T3 so that for any point x ∈ H2 the orthogonal bisectors of the three segments with endpoints x, Ti(x) intersect. This is equivalent to proving the properness of certain algebraic sets. As a corollary, we give a new proof for the existence and density of generic fundamental polygons for cocompact Fuchsian groups.engjournal articlehttp://topology.auburn.edu/tp/reprints/v33/tp33006p1.pdfhttp://topology.auburn.edu/tp/restricted access514Fuchsian groups and automorphic functionsModuli of Riemann surfacesTeichmüller theoryGeometría1204 Geometría