On a H\"older constant in the theory of quasiconformal mappings
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constantolderboundarydiskestimatefracidentityk-quasiconformal
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A K-quasiconformal selfmap of the unit disk with identity boundary values satisfies the H\"older estimate $|f(z)-f(w)| \leq 4^{1-1/K} |z-w|^{1/K}$. The constant $4^{1-\frac{1}{K}}$ is sharp.
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