This preview shows page 1. Sign up to view the full content.
Unformatted text preview:  f j ( z )  2 on a disc centered around z (and included in U ). Then show the f j are uniformly bounded on compact sets. (4) Consider f ( z ) = 1 2 ( z + 1 /z ). Show that f gives a conformal equivalence between D (0 , 1) and C {}\ [1 , 1]. 1 What happens with circles D (0 ,r ) under this map? And what with the linesections [0 , 1) originating from the origin (for D (0 , 1))? Hint: conic sections. 1 In a coincidence, this conformal map was used in a talk I went to today (after I made the problem set). 1...
View
Full
Document
This document was uploaded on 12/08/2010.
 Spring '09

Click to edit the document details