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We study the removability of compact sets for continuous Sobolev functions.
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Devaney R., Rocha M., Siegmund S.: Rational maps with generalized Sierpiński gasket Julia sets. Topology Appl. 154
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Astala K., Iwaniec T., Martin G.: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane. Princeton University Press, Princeton, NJ (2009)
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Ntalampekos, D.: Non-removability of Sierpiński carpets. Preprint arXiv:1809.05605 (2018)
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Ntalampekos, D.: Non-removability of the Sierpiński gasket. Invent. Math. 216
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Ntalampekos, D., Wu J.-M.: Non-removability of Sierpiński spaces. Proc. Amer. Math. Soc., to appear, https://doi.org/10.1090/proc/14698 (2019)
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