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Analytic in an annulus

  1. Jan 17, 2010 #1
    1. if f(z) is analytic on the unit disk D. Suppose there is an annulus U={r<|z|<1} such that the restriction of f(z) to U is one-to-one. Show that f(z) is one-to-one on D.



    2. Relevant equations

    I am having trouble using the hypotheseis "f is one-to-one" I believe. I cannot think other than this implying that f'(z) is nonzero, but this does not seem to suffice





    3. The attempt at a solution
    I am trying to use Swarz lemma in conjunction with Identity theorem (that is showing that two functions agree on an infinite set), but I
     
  2. jcsd
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