Hi, I know this one is not too hard, but I've been stuck for a while:(adsbygoogle = window.adsbygoogle || []).push({});

Say f is holomorphic and non-constant on the closed unit disc D(0,1),

and |f|=1 on the boundary of the disk (so that, e.g., by the MVT,

f maps the disk into itself) . Is it the case that f maps

the disk _onto_ itself?

I have thought of trying to show that the integral:

∫_D (f'(z)dz/(f(z)-a ) is non-zero , for a in the interior of D.

i.e., the winding number of f(z) about any point on the disk is

non-zero. But I can't see how to show this. Any Ideas?

I am trying to use the fact that if f is analytic, then f is a finite product of Blaschke

factors , but it still does not add up. Any ideas?

Thanks in Advance.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Holomorphic Maps on D(0,1)

Loading...

Similar Threads - Holomorphic Maps | Date |
---|---|

Holomorphic function on the unit disc | May 1, 2012 |

Is this function holomorphic? | Dec 3, 2011 |

Curl and divergence of the conjugate of an holomorphic function | Aug 11, 2011 |

Complex analysis/holomorphic/conformal map | Mar 23, 2010 |

Holomorphic map | May 11, 2007 |

**Physics Forums - The Fusion of Science and Community**