Abstract
We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one. Furthermore, we apply this result to the theory of extremal quasiconformal mappings. Let [µ] be a point in the universal Teichmuller space such that the Hausdorff dimension of f µ(ϖΔ) is bigger than one. We show that for every k n ∈ (0, 1) and polygonal differentials φ n , n = 1, 2, …, the sequence $$ \{ [k_n \frac{{\overline {\phi _n } }} {{|\phi _n |}}]\} $$ cannot converge to [µ] under the Teichmuller metric.
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