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+--- Thread: Generalized Bieberbach conjectures ? (/showthread.php?tid=805)
Generalized Bieberbach conjectures ? - tommy1729 - 08/12/2013
I wanted to say that I believe tetration is related to generalizations of the Bieberbach conjecture/de Branges theorem , Koebe quarter theorem and related.
For instance Let U be the unit circle , let V be a smaller circle that touches the unit circle from the inside. The "moonshaped " area ( this has a name right ? ) Is called A. Let the open set A be mapped injectively to the complex plane by the function f(z).
Then D^n f(z) dz satisfies ....
Now by riemann mappings and inversing functions we end up with a branch for a superfunction.
And the conjectured properties must be carried along in a transformed way.
This "moonshaped conjecture " might already have a name , but if not I call it tommy's moonshine conjecture for now , although I havent figured out the details of even the precise statement.
This is something I have not seen adressed on the forum yet so I found it necc to mention it.
regards
tommy1729