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23h
accepted On the geometry of roots of a sum of complex linear fractions
23h
comment On the geometry of roots of a sum of complex linear fractions
Thanks for the reference. It seems difficult though to obtain a geometrical interpretation from this lemma. For what I want, I think Theorem 8.2, p.32, is more interesting.
2d
revised On the geometry of roots of a sum of complex linear fractions
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2d
revised On the geometry of roots of a sum of complex linear fractions
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2d
asked On the geometry of roots of a sum of complex linear fractions
Mar
26
comment The Riemann mapping theorem via extremal problems
What I am interested in here is just the particular case $n=1$ of Ahlfor's theorem, without any assumption on the boundary of the domain.
Mar
25
comment The Riemann mapping theorem via extremal problems
Yes indeed, the Riemann mapping theorem is a direct consequence of Ahlfor's theorem on the properties of the Ahlfors function on $n$-connected domains. However, as you mention, every proof I know of this theorem uses analyticity of the boundary, which requires the Riemann mapping theorem. So this does not answer the question. The remark about the Bergman kernel is very interesting, I will look it up. Thank you.
Mar
24
revised The Riemann mapping theorem via extremal problems
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Mar
19
revised The Riemann mapping theorem via extremal problems
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Mar
18
revised The Riemann mapping theorem via extremal problems
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Mar
17
asked The Riemann mapping theorem via extremal problems
Feb
17
comment $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$ if and only if $f$ is linear
@AlexandreEremenko : After Theorem 1.3 of the paper mentioned in my answer, it is written The main contribution of the Landau-Toeplitz paper is perhaps its elucidation of the extremal case.
Feb
16
answered $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$ if and only if $f$ is linear
Feb
7
comment Examples of common false beliefs in mathematics.
@MartinBrandenburg : What does it mean for an assumption to be incorrect or correct?
Jan
5
comment Arakelian's approximation theorem
I just took a quick look at the paper and it seems that the proof only uses the fact that the modulus of the integral is small, not that the integral of the modulus is small. Perhaps it is a typo.
Nov
11
comment About the Riemann integrability of composite functions
I just saw this very old question, but I'm not sure I understand your doubt about the existence of $g$ : Can't you just take $g(x)$ the distance from $x$ to a Cantor set $C$ of positive measure?
Nov
8
comment Integral and conformal mappings II
I think user36162 is right. I don't see why $I_n$ would diverge since $f_n'$ must be bounded in $D$.
Nov
8
comment Uniform convergence of conformal mappings
You're right of course, I was confused and my answer was wrong. Thank you for pointing it out. Great answer, +1 !
Nov
7
comment Uniform convergence of conformal mappings
@PietroMajer : Surely this is what is meant. I assumed it in my answer.
Nov
3
comment A question on Koebe theorem
@ToddTrimble : Thank you!