Timeline for Extension of conformal map and annulus
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 24, 2015 at 14:19 | vote | accept | Clem. | ||
| Apr 23, 2015 at 22:36 | comment | added | Alexandre Eremenko | What do you mean by "circles"?? | |
| Apr 23, 2015 at 15:10 | answer | added | Lasse Rempe | timeline score: 3 | |
| Apr 23, 2015 at 14:59 | comment | added | Clem. | The question more precise should be : is there a conformal map $\psi$ such that a control in the sense I gave is possible (this is not so for arbitrary maps : one can find easy examples sending à circle to a region close to the boundary) ? | |
| Apr 23, 2015 at 13:22 | comment | added | Clem. | Yes, I realised the question wasn't well posed. I was meaning an arbitrary doubly connected region (that is bounded by 2 non-intersecting Jordan curves). So my question can be modified a bit : suppose I know the modulus of $\Omega$ (that is the real $r$). Take an arbitrary conformal map $\psi$ from the interior of $C_2$ to $D$. In general $C_1$ is not sent to a circle. But can I have a control of this Jordan curve though ? For example, if I know $\Omega$ is not thin (say $r \leq 1-\varepsilon$), is it possible to say that $\psi(C_1)$ is contained in some disc $D(1-\delta)$ ($\delta>0$) ? | |
| Apr 23, 2015 at 12:14 | comment | added | Misha | As you saw in two conflicting answers, the answer depends on what do you mean by a circle (round or topological). | |
| Apr 23, 2015 at 10:29 | answer | added | Neil Strickland | timeline score: 2 | |
| Apr 23, 2015 at 9:45 | history | edited | Joonas Ilmavirta | CC BY-SA 3.0 |
deleted 2 characters in body
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| Apr 23, 2015 at 6:13 | answer | added | Robert Israel | timeline score: 1 | |
| Apr 23, 2015 at 6:03 | history | asked | Clem. | CC BY-SA 3.0 |