Abstract
We study variations of the first nontrivial eigenvalue of the two-dimensional p-Laplace operator, p > 2, generated by measure preserving quasiconformal mappings. The study is based on the geometric theory of composition operators in Sobolev spaces and sharp embedding theorems. Using a sharp version of the reverse Holder inequality, we obtain a lower estimate for the first nontrivial eigenvalue in the case of Ahlfors type domains.
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