5 sample documents related to MATH 612

• 
  2007-05-03.pdf

  Cornell MATH 612
  

  Math 612 homework assignment 12 due 2007-05-03 at 3 pm 1. Prove the following statements. (i) Let X and Y be Riemann surfaces and f, g : X Y holomorphic maps. If f = g on a set with a limit point in X, then f = g. (ii) Let X and Y be Riemann surf
   
• 
  2007-04-05.pdf

  Cornell MATH 612
  

  Math 612 homework assignment 8 due 2007-04-05 at 3 pm For z1 , z2 D put (z1 , z2 ) = inf{L()}, where ranges over all piecewise C1 paths in D joining z1 to z2 . Let D = D(0, 1) be the open unit disc. For any piecewise C1 path : [a, b] D dene |
   
• 
  2007-03-15.pdf

  Cornell MATH 612
  

  Math 612 homework assignment 6 due 2007-03-15 at 3 pm 1. Let X and Y be metric spaces and (fn ) a sequence of (not necessarily continuous) maps fn : X Y. We say (fn ) converges continuously to f : X Y (in brief, fn f continuously) if limn fn (x
   
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  2007-02-17.pdf

  Cornell MATH 612
  

  Math 612 homework assignment 3 due 2007-02-15 at 3 pm 1. Rudin 10: 2, 4, 5, 16, 17. ^ A circle in the Riemann sphere C is a subset which is either a circle in C or a set of the form l {}, where l is a straight line in C. Equivalently, a circle ^
   
• 
  2007-05-10.pdf

  Cornell MATH 612
  

  Math 612 take-home nal exam due 2007-05-10 at 3 pm Please observe the following rules. Do not collaborate. Do not consult sources other than the textbook. You may consult with me and use all results covered in the book, in class, or in the homewor