Timeline for Zeros of a holomorphic function
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2011 at 16:02 | comment | added | Analyst2 | Thank you, but could you elaborate a little on why $f(C)$ equals the unit circle? | |
| Jan 3, 2011 at 16:20 | comment | added | Bill Thurston | To translate this into topological language: $f$ is a map from $\Omega$ to the unit disk that takes boundary to boundary. (The image of $\Omega$ is in the disk by the maximum principle). The number of zeros (counted with multiplicity) is the degree of the map. The degree of the map equals the degree of the map on the boundary, which must be at least $m+1$ (since analyticity forces the map to be monotone increasing on each boundary component) | |
| Jan 3, 2011 at 16:12 | history | answered | J.C. Ottem | CC BY-SA 2.5 |