Timeline for What $Re(f(z))=c$ can be if $f$ is a holomorphic function ?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2010 at 22:42 | vote | accept | Leandro | ||
| Nov 26, 2010 at 17:17 | comment | added | timur | Yes, but they may intersect each other. Let us say $z$ is a critical point if $f'(z)=0$, and let us treat the set $\mathrm{Re}f(z)=c$ as the preimage of the curve $\mathrm{Re}w=c$. Then at non-critical points $f$ is locally invertible, so the curve $\mathrm{Re}w=c$ has differentiable curve as its preimage near non-critical points. Now near its critical points $f$ is $n$-to-$1$, and so the curve $\mathrm{Re}w=c$ will have as its preimage $n$ copies of differentiable curves, which all intersect (forming an even angle between them) at the critical point. | |
| Nov 26, 2010 at 8:49 | answer | added | Bruno Martelli | timeline score: 5 | |
| Nov 26, 2010 at 6:30 | answer | added | Andreas Thom | timeline score: 5 | |
| Nov 26, 2010 at 4:24 | history | asked | Leandro | CC BY-SA 2.5 |