Riemann Surfaces: Notes of Lectures Given at the University of Minnesota, Winter and Spring Quarters, 1968School of Mathematics, Institute of Technology, University of Minnesota, 1970 - Quasiconformal mappings - 226 pages |
Common terms and phrases
1817 LIBRARIES analytic function Beltrami differential bordered Riemann surface boundary point boundary values bounded closed curve complex dilatation conclude conformal structure conformally equivalent contains continuous convergent countable cover transformation group covering S,a definition denote differential of G exists extended plane f₁ f₂ finite number finite plane fixed point free function f G₁ G₂ Green's function group G harmonic function harmonic measure Hence homotopic hyperbolic identity mapping integral invariant isomorphic Lemma Let f Let G lim sup locally homeomorphic mapping f mapping theorem maximal dilatation maximum principle MICHIGAN modulo monodromy theorem neighborhood normal open set P₁ P₂ parabolic parameter parametric disc plane domain Proof properly discontinuous prove relatively compact domain Riemann surface S₁ S₂ Schwarzian derivative simply connected singularity smooth covering surface strong maximum principle subgroup of F subharmonic function subset Teichmüller space topology triples unit disc universal covering surface unlimited covering surface