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We study the variation of the Neumann eigenvalues of the $p$-Laplace operatorunder quasiconformal perturbations of space domains. This study allows toobtain lower estimates of the Neumann eigenvalues in fractal type domains. Thesuggested approach is based on the geometric theory of composition operators inconnections with the quasiconformal mapping theory.

Space Quasiconformal Mappings and Neumann Eigenvalues in Fractal Domains