New isoperimetric inequalities between Stekloff eigenvalues and function theoretic quantities in simply and multiply connected domains are derived. They sharpen on the one hand well-known isoperimetric inequalities in some cases and given on the other hand both-sided estimates for function theoretic quantities. In the simply connected case both-sided estimates for Stekloff eigenvalues are given based on a general monotonicity principle.
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Bodo Dittmar, Stekloffsche Eigenwerte und konforme Abbildungen. Z. Anal. Anwend. 7 (1988), no. 2, pp. 149–163DOI 10.4171/ZAA/292