(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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Koebe function | Article about Koebe function by The Free Dictionary
I do not understand your comment about the Koebe function in the edit. How does it arise? Email Kebe, but never shown. Is this obviously wrong? The removed set is shown below in blue:. However, of course this changes the derivative at the origin I’ll revise my question to make that clear.
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Are you assuming that the derivative at the origin is equal to one? But I don’t know if these modified Koebe functions are extremal in the case where the functions are required to fix The removed set is shown below in kowbe Home Questions Tags Users Unanswered.
In particular, there is no extremal map. It seems like a rather odd condition, unless you are assuming your functions to be real on the real axis. In anycase, I have very specific normalization conditions, and just precomposing by rotation does not preserve them.