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chapter 4, proposition 4.2.7 in Hubbard's Teichmuller Theory book, volume 1, he proves : Let $U,V$ be open in $C, f:U \to V $ be a homeomorphism and the restriction of $f$ on $U \backslash l$ is $K$ quasiconformal …

I was studying Theorem 4.4.1 from John H. Hubbard's Teichmuller Theory, vol I, Theorem 4.4.1 ( P. 129 ) which states : Let $X,Y$ be two hyperbolic Riemann surfaces with hyperbolic metrics $d_X,d_Y$ r …

Hello, This question is related to Chapter V, lemma 3 on page 54 of Lars Ahlfors' 'Lectures on Quasiconformal mappings' which states : If $\mu:\mathbb{C}\to \mathbb{D} \in W^{1,p}(\mathbb{C}), p …

Hello, I asked this question before, but didn't get any response, so I took the liberty of asking once again , with slightly modified version of the question: Consider an orientation-preserving quasiconformal … ( Look at Examples 15.1 in the book "Elliptic PDE and Quasiconformal Mappings" by K. Asltala, T. Iwaniec and G. Martin. http://books.google.com/books? …

I would be happy if the answer to (I) is yes though, because then we might look at the "smooth" subset of Teichmuller spaces : {restriction of $\mu$-quasiconformal maps fixing $1,-1,i$ to $S^1,\mu \in …

Let $f:S^n\to C$ be a continuous function, $n\geq 1$. When $n=1$, this is a well-known theorem, called Kellog's theorem (or sometimes Kellog-Warschawski's theorem) which states the following Theorem: …

$Qn#1 $ : Let $f:U\to V$ be a $K$ quasiconformal homeomorphism ( NOT diffeomorphism ) of plane open subsets of $C$. …

Hello, this question might sound a little vague, but I still dare to state , and I am basically requesting for some reference: Let us consider the orientation-preserving homeomorphic solutions $f: D …