Re: Complex analysis question

On Sun, 22 Jul 2007, S Gupta wrote:

Does there exist a surjective holomorphic function from >>the unit disk onto the whole complex plane?

Yes, there does.

Hint...
Some of the standard conformal maps can be used to take >the
disk to the complex plane minus a half-line. Modify this >a bit so
that it's not one-to-one.

Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

So, for example, if we map the unit disk to the upper half plane first (bijectively), then apply the map z^4, so that it spins around 4(pi) degrees, and has a removable singularity at 0, and thus holomorphic on the whole plane?

Is that what you meant?

Thanks again
.

Relevant Pages

  • Re: Complex analysis question
    ... Some of the standard conformal maps can be used to take>the ... disk to the complex plane minus a half-line. ... Modify this>a bit so ...
    (sci.math)
  • Re: Complex analysis question
    ... On Sun, 22 Jul 2007, S Gupta wrote: ... Some of the standard conformal maps can be used to take the ... disk to the complex plane minus a half-line. ...
    (sci.math)
  • Re: Complex analysis question
    ... On Mon, 23 Jul 2007, S Gupta wrote: ... Some of the standard conformal maps can be used to take>the ... disk to the complex plane minus a half-line. ...
    (sci.math)
  • Re: Complex analysis question
    ... Some of the standard conformal maps can be used to take the ... disk to the complex plane minus a half-line. ...
    (sci.math)
  • Re: OE6 dont save modifcation on attachment
    ... "Sorin TENE" wrote in message ... I've look in Temporary Internet Folder (it is set to 1Gb disk space), ... To modify an attachment you must drag and driop it out of the message, ...
    (microsoft.public.windows.inetexplorer.ie6_outlookexpress)