(c) Thinking of the Koebe function f as a map from the unit disk |z| < 1 to the complex plane, where does it fail to be one-to-one? Investigate this by looking at the. Looking for Koebe function? Find out information about Koebe function. The analytic function k = z -2= z + 2 z 2+ 3 z 3+ ⋯, that maps the unit disk onto the entire. Nonunivalent generalized Koebe function . of the Japan Academy, Series A, Mathematical Sciences, ; On harmonic combination of univalent functions.
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If you are concerned about the consequences of said adjustment, work differently: Braindead 3, 17 Email Required, but never shown.
I’ll revise my question to make that clear.
complex analysis – Image of koebe map – Mathematics Stack Exchange
The extremal case is given by the Koebe function or one of its rotations. Home Questions Tags Users Unanswered.
Koebe quarter theorem
But I don’t know if these modified Koebe functions are extremal in the case where the functions are required to fix However, of course this changes the derivative at the origin It seems like a rather odd condition, unless you are assuming your functions to be real on the real axis.
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Koebe quarter theorem – Wikipedia
Your function should have az also in the numerator. In that book, Koebe function and all of its “rotations” are functions of the form I wrote in my edit. This is in response to a comment about rotating the Koebe function