bio | website | mat.ulaval.ca/… |
---|---|---|
location | Québec | |
age | ||
visits | member for | 4 years, 10 months |
seen | 5 hours ago | |
stats | profile views | 1,794 |
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 |