bio  website  math.sunysb.edu/~myounsi 

location  Stony Brook, NY, USA  
age  
visits  member for  5 years, 7 months 
seen  1 hour ago  
stats  profile views  1,976 
I am currently a NSERC postdoctoral fellow at Stony Brook University.
1d

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Conformal map and Jordan curve
Well what if $\Omega$ is the whole plane and $\gamma$ is not a circle? In this case, such an $f$ would be linear, so that $f(\gamma)$ cannot be a circle. 
1d

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Conformal map and Jordan curve
Not in general, of course, just because the curve $\gamma$ needs to be analytic if there is such a conformal map $f$. 
Apr 19 
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If $f$ is separately holomorphic on $\Omega$ then $f\in\mathcal{C}^0(\bar\Omega)\Leftrightarrow f\in L^1(\Omega)$
What do you mean by "Hartog's theorem is not allowed"? 
Jan 12 
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This inequality why can't solve it by now (Only four variables inequality)?
@AdamP.Goucher : But in your book "Mathematical Olympiad Dark Arts", you say "Hence [by Delzell's algorithm] it is theoretically possible to prove any inequality involving rational functions simply by reducing it to the sum of squares inequality. However, this approach is similar in its impracticality to building an automobile using Stone Age tools." As for the present problem, I would be quite interested to see the automobile built more efficiently..! 
Jan 12 
revised 
Analytic diffeomorphisms of the circle from complex domains
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Jan 12 
revised 
Analytic diffeomorphisms of the circle from complex domains
added 803 characters in body 
Jan 12 
answered  Analytic diffeomorphisms of the circle from complex domains 
Dec 12 
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Bound areas of disks with respect to a quadratic differential
@DylanThurston : I'm glad I could help. 
Dec 12 
revised 
Bound areas of disks with respect to a quadratic differential
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Dec 12 
revised 
Bound areas of disks with respect to a quadratic differential
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Dec 12 
comment 
Bound areas of disks with respect to a quadratic differential
Yes, I made a silly mistake. I corrected my answer, hopefully it works now. 
Dec 12 
revised 
Bound areas of disks with respect to a quadratic differential
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Dec 12 
answered  Bound areas of disks with respect to a quadratic differential 
Dec 8 
accepted  Is this infinite series related to some wellknown special functions? 
Dec 8 
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Is this infinite series related to some wellknown special functions?
Great, thank you! +1 
Dec 8 
awarded  Good Answer 
Dec 4 
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Starshapeness of polynomial tracts with respect to the (entire collection of) critical points contained in the tract
Do you assume that $G$ is connected? 
Dec 3 
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Starshapeness of polynomial tracts with respect to the (entire collection of) critical points contained in the tract
There is also a simple proof using potential theory in the book "Potential theory in the complex plane" by Thomas Ransford, Theorem 5.5.8. I don't have access to Walsh's book right now, so I don't know if the proof is the same. 
Nov 14 
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Applications of the Small and Great Theorems of Picard
@GHfromMO Ah, I didn't realize you were talking about meromorphic functions. Good point! The argument works for entire functions, but I don't know how to prove the result for meromorphic functions using Picard's theorem. 
Nov 14 
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Applications of the Small and Great Theorems of Picard
@GHfromMO : From the factorization $1=\prod_{j=1}^n (f\zeta_j g)$ where $\zeta_1,\dots,\zeta_n$ are the $n$ roots of $z^n+1=0$, it follows that $f/g$ is a meromorphic function that omits the values $\zeta_1,\dots,\zeta_n$, and hence must be constant by Picard's theorem. From this it follows easily that both $f$ and $g$ must be constant. 