1

I was wondering while studying for my complex analysis finals, on chapter on orientation, is it possible to find some holomorphic function on the unit closed disk which sends the unit circle with the counterclockwise orientation into the unit circle with clockwise orientation?

It seems like an interesting question to ponder about, but I cannot think of any as of now, I was wondering if anyone could give me an example of a function which could do this?

Aurora Borealis
  • 1,747
  • 1
    Holomorphic functions preserve the orientation... – Martín-Blas Pérez Pinilla Apr 19 '18 at 09:50
  • My comment is that the assertion is false, as the Argument principle would necessarily imply that $f$ (the 'function') would have poles within the unit circle. –  Apr 19 '18 at 09:52
  • Ok thank you for the response, so how could one give a formal proof which implies that this question is false? – Aurora Borealis Apr 19 '18 at 10:04
  • @Kevin ok I am still stuck at proving this rigorously, sure intuitively I can see why this might be the case. Any help would be appreciated cause this problem really will help me understand some orientation concepts in complex analysis. – Aurora Borealis Apr 20 '18 at 02:49
  • Yes I know, I asked after I got no answers for this one which was also made by me.... – Aurora Borealis May 02 '18 at 15:17

0 Answers0