All Questions
8 questions
12
votes
2
answers
2k
views
Universal covering of a 2-sphere without $n$ points
Let $X$ be the $\mathbb{C}\mathbb{P}^1$ with $n$ points deleted. Let $n\geq 3$. If I understand correctly, the universal covering of $X$ is isomorphic to the upper half plane as a complex analytic ...
- 21.8k
8
votes
2
answers
328
views
Equivalence of definitions of quasiconformal surfaces?
I have been reading John H. Hubbard's book Teichmüller Theory vol. 1 and I am a little bit concerned with his definition of quasiconformal surface.
Definition: A quasiconformal surface $S$ is a ...
- 298
4
votes
1
answer
279
views
Shrinking the boundary of a Riemann surface
Let $X$ be a compact Riemann surface with boundary. Let us shrink each connected component of the boundary into a point. We get a closed topological surface $Z$ with several marked points (which came ...
- 21.8k
4
votes
1
answer
503
views
Characterization of the moduli space of the pair of pants in terms of the modules of the extremal ring domains
Hi, I was thinking about the following question ; I will appreciate it if somebody can give me a full or partial answer or can at least cite any reference(s)/ papers etc :
By $ \bar{P} $ , we ...
- 1,471
3
votes
1
answer
907
views
The version of Montel's theorem used in the proof of Jenkins-Strebel differential
Hello,
I am afraid that my main question might be a bit too elementary, but still I ask :
In short, my question is "what is the version of Montel's theorem for a family of holomorphic maps from an ...
- 1,471
2
votes
2
answers
910
views
Complex structure on a punctured torus giving a complex structure on the torus?
Can anyone provide an idea of the proof or a reference of the fact that a complex structure on the once punctured torus extends to one on the torus?
In other words, the Teichmuller space of the ...
- 2,964
1
vote
0
answers
77
views
Computing some closed trajectories of meromorphic quadratic differentials
I'm learning about meromorphic (!) quadratic differentials on Riemann surfaces, and would like to determine the closed trajectories [EDIT: I mean closed geodesics, not just closed trajectories; ...
- 121
0
votes
1
answer
159
views
Teichmüller theory for open surfaces?
I have a rather straightforward and perhaps somewhat naive question: Is there a Teichmüller theory for open surfaces?
My motivation basically is that I would like to find out more about the "...
- 7,127