Timeline for Groups of conformal isomorphisms of simply connected surfaces
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2023 at 2:19 | comment | added | Alexandre Eremenko | Very simple. The map $f$ has finitely many zeros and poles in $C$. Let $g$ be the rational function with the same zeros and poles in $C$ (counting multiplicity). Then $h=f/g$ has no zeros or poles in $C$. If $h(\infty)$ is infinite, consider $g/f$ instead. A bounded holomorphic function on the sphere must be constant. (Both the Maximum Principle and Liouville theorem which can be used to make this conclusion have simple algebraic proofs). | |
| Apr 28, 2023 at 16:42 | comment | added | Vít Tuček | How do you prove, using only essentially elementary algebra, that any holomorphic map from sphere to itself is meromorphic? :) | |
| Apr 28, 2023 at 12:29 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
added 58 characters in body
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| Apr 28, 2023 at 12:18 | history | answered | Alexandre Eremenko | CC BY-SA 4.0 |