All Questions
Tagged with teichmueller-theory quasiconformal-maps
9 questions
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Existence of extremal map in teichmuller class
Let $R$ be a Riemann surface, and define two quasiconformal maps $f_i : R \rightarrow R_i, i=1,2$ to be equivalent if there exists a conformal map $c : R_0 \rightarrow R_1$ and a homotopy $g_t : R \...
- 1,703
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1
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98
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Convergence in Teichmüller space
Question 1
Let $X$ be a compact hyperbolic Riemann surface and let $\{[\mu_n]\}$ be a sequence of points in the Teichmüller space $\mathcal T(X)$.
Further, assume there are maps $f_n:X \xrightarrow{q....
- 829
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70
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Does moving a small enough distance in Teichmüller space change the marking?
Let $S_{g}$ be a genus $g$ closed Riemann surface. The Teichmüller space $\mathcal{T}(S_{g})$ is the set of all pairs $(X,\phi)$ where $X$ is a Riemann surface of genus $g$ and $\phi : S_{g} \...
- 560
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Question about Hubbard's analytic definition of quasiconformality. Aren't weak derivatives only defined up to a set of measure zero?
I'm a bit confused about something that appears in the fourth chapter of Hubbard's Teichmüller Theory text. In his statement of Weyl's lemma, he says that if $f$ is a distribution whose weak/...
- 1,119
4
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279
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Homeomorphism Between Closed Riemann Surfaces Homotopic to Quasiconformal Mapping
I'm re-reading a paper of Bers and for the second time, and I am yet again confused about the claim in the title, which Bers declares to be easy to prove.
For context, I'll lay out some terminology....
- 401
4
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1
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595
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Could someone explain to me what a Teichmuller Space is?
In the simplest terms possible, for someone who understands the basics of Manifolds, Topology, but barely any of the more complicated topics.
I've been using the following:
http://homeowmorphism.com/...
- 101
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1
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308
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Uniformly convergent sequence of quasiconformal mappings
Let $G \subseteq \mathbb{C}$ be a domain (one may assume that $G$ is bounded and simply connected, if needed). Suppose $(f_n)_{n \in \mathbb{N}}$ is a sequence of bounded (i.e. $\sup_{z \in G} |f_n(z)|...
- 745
2
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1
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98
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How to show this mapping is quasiconformal. And the integrability of the gradient.
A complex map $f$ on the unit disk defined as $f(re^{i\theta})=r^ke^{i\theta}$ where $k>1$. I hope to know how to show this map is quasiconformal and what is the largest $p$ such that the gradient ...
- 137
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$f$ conformal $\implies$ $f$ ACL?
In An Introduction to Teichmüller Spaces, by Imayoshi and Taniguchi, we have the following definition for an absolutely continuous function:
where, I suppose, a function $g:I\to \mathbb{C}$, $I \...
- 2,847