Timeline for Show properness of Ahlfors map
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 9, 2014 at 9:46 | comment | added | Josh | Maybe I found a way to use the above mentioned surface G, in particular that $G$ is relatively compact. There is a theorem like "If $f: X \longrightarrow Y$ is a continuous mapping between topological spaces and $W$ is an open relatively compact subset of $X$, then the induced map $W \backslash f^{-1}(f(\partial W)) \longrightarrow Y \backslash f(\partial W)$ is proper". So it must be proved that there exists a map $\overline{\phi} : \overline{G} \longrightarrow \overline{\Delta}$ with $\overline{\phi} = \phi$ in $G$ | |
| Oct 10, 2014 at 18:01 | comment | added | Malik Younsi | I don't understand what you mean by that. In the case of planar domains bounded by $n$ disjoint analytic Jordan curves, the Ahlfors function is proper of degree $n$, so it has $n$ zeros. This is usually what is proved in order to obtain properness. | |
| Oct 10, 2014 at 15:01 | comment | added | user59344 | Malik Younsi, regarding the above question about the properness of Ahlfors map, dont you think that we need to have knowledge about zeros of Ahlfors map? Thanks | |
| Jun 26, 2014 at 12:12 | comment | added | Malik Younsi | @Josh : You're welcome. I don't think there is a simple, easy way to prove properness of the Ahlfors map. | |
| Jun 26, 2014 at 9:59 | comment | added | Josh | Thanks for your answer, i hoped that there would be a way to show that the Ahlfors map is proper in a more directly sense, using the definition of properness and i hoped that this proof would allow a generalization to Riemann surfaces. | |
| Jun 25, 2014 at 13:59 | history | answered | Malik Younsi | CC BY-SA 3.0 |