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Two disks maximize the third Robin eigenvalue: positive parameters

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GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

In this talk, I will discuss the maximization of third Robin eigenvalue for negative parameters. The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the corresponding eigenvalue of a disjoint union of two equal disks, for Robin parameters in [-4\pi,4\pi]. This sharp inequality was known previously only for non-positive parameters by Girouard and Laugesen. This difficulty is overcome by means of a degree-theoretic approach. This talk is based on a joint work with R. Laugesen

This talk is part of the Isaac Newton Institute Seminar Series series.

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