Isoperimetric inequalities and variations on Schwarz's Lemma
نویسنده
چکیده
In this note we prove a version of the classical Schwarz lemma for the first eigenvalue of the Laplacian with Dirichlet boundary data. A key ingredient in our proof is an isoperimetric inequality for the first eigenfunction, due to Payne and Rayner, which we reinterpret as an isoperimetric inequality for a (singular) conformal metric on a bounded domain in the plane.
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تاریخ انتشار 2010