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 |
Contents
Boundary of a Riemann surface | 6 |
II | 9 |
Covering surfaces and the fundamental group | 15 |
8 other sections not shown
Common terms and phrases
analytic arbitrary assume Beltrami boundary boundary point bounded called choose closed compact complex conclude condition conformal mapping conformal structure conformally equivalent Consequently consider constant contains continuous convergent corresponding countable cover transformation group covering surface curve defined definition denote determine differential dilatation direct discontinuous domain elements equation exists extended fixed point follows fundamental G₂ given Green's function group G harmonic function Hence holds homeomorphism homotopic hyperbolic identity implies induced integral invariant isomorphic Lemma LIBRARIES lies limit linear locally maximum principle MICHIGAN neighborhood normal obtain open set origin parabolic parameter parametric disc plane plane domain possible problem projection Proof prove relatively remark result Riemann surface S₁ S₂ satisfies sequence side simply connected singularity smooth covering surface solution space subharmonic subset Theorem triples unique unit disc universal covering surface vanishes whole