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bio website mat.ulaval.ca/…
location Québec
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visits member for 4 years, 10 months
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Jul
23
comment A special case of the uniformization theorem
This is a nice proof using PDEs! I am not familiar with the fact that "Since $\langle \delta', 1\rangle = 0$, on a compact manifold we can solve $\Delta u = \delta'$" Do you know a reference for this?
Jul
10
comment A special case of the uniformization theorem
Thank you both for the additional comments. I was not aware of this approach via conformal welding.
Jul
8
accepted A special case of the uniformization theorem
Jul
8
comment A special case of the uniformization theorem
I did not know that one could use Riemann-Roch to prove this. Thank you!
Jul
5
comment A special case of the uniformization theorem
Yes, I did. The proof that the fact that you mention implies that a Riemann surface homeomorphic to the sphere is conformally equivalent to the sphere is 5 pages long, which is why I thought I was missing something when you wrote immediately implies
Jul
4
comment A special case of the uniformization theorem
Thank you very much for the reference. However, I don't see how the conformal welding fact that you mention immediately implies that a Riemann surface homeomorphic to the sphere is conformally equivalent. The opposite is clearly true though. Could you add some details?
Jul
4
asked A special case of the uniformization theorem
Jul
2
awarded  Curious
Jun
26
comment Show properness of Ahlfors map
@Josh : You're welcome. I don't think there is a simple, easy way to prove properness of the Ahlfors map.
Jun
25
answered Show properness of Ahlfors map
May
21
comment Absolute value inequality for complex numbers
Very nice trick! +1
Apr
17
accepted On the geometry of roots of a sum of complex linear fractions
Apr
17
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.
Apr
15
revised On the geometry of roots of a sum of complex linear fractions
edited tags
Apr
15
revised On the geometry of roots of a sum of complex linear fractions
added 342 characters in body
Apr
15
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
deleted 37 characters in body
Mar
19
revised The Riemann mapping theorem via extremal problems
deleted 35 characters in body; edited tags