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arXiv · 2403.13426

Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics

Jade Brisson·Bruno Colbois·Katie Gittins
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Abstract

We investigate upper bounds for the spectral ratios and gaps for the Steklov eigenvalues of balls with revolution-type metrics. We do not impose conditions on the Ricci curvature or on the convexity of the boundary. We obtain optimal upper bounds for the Steklov spectral ratios in dimensions 3 and higher. In dimension 3, we also obtain optimal upper bounds for the Steklov spectral gaps. By imposing additional constraints on the metric, we obtain upper bounds for the Steklov spectral gaps in dimensions 4 and higher.

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Jade Brisson, Bruno Colbois, Katie Gittins. 2024-03-20. Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics. https://doi.org/10.4153/s0008439524000778

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