Abstract
In [1–3] some analytical properties were investigated of the Von Koch curve Γ θ , θ ∈ \((0,\tfrac{\pi } {4}) \) . In particular, it was shown that Γ θ is quasiconformal and not AC-removable. The natural question arises: Can one find a quasiconformal and not AC-removable curve essentially different from Γ θ in the sense that it is not diffeomorphic to Γ θ ? The present paper is an answer to the question. Namely, we construct a quasiconformal curve, calling the “Frog,” which is not AC-removable and not diffeomorphic to Γ θ for any θ ∈ \((0,\tfrac{\pi } {4}) \).
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Original Russian Text Copyright © 2012 Gospodarczyk A.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 794–804, July–August, 2012.
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Gospodarczyk, A. The fractal “Frog”. Sib Math J 53, 635–644 (2012). https://doi.org/10.1134/S0037446612040064
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DOI: https://doi.org/10.1134/S0037446612040064