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

Brisson, Jade; Colbois, Bruno; Gittins, Katie

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.

Citation

Brisson, J., Colbois, B., & Gittins, K. (2025). Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics. Canadian Mathematical Bulletin, 68(2), 492-511. https://doi.org/10.4153/S0008439524000778

• Journal Article Type: Article
• Acceptance Date: Oct 28, 2024
• Online Publication Date: Jan 14, 2025
• Publication Date: 2025-06
• Deposit Date: Nov 25, 2024
• Publicly Available Date: Jan 14, 2025
• Journal: Canadian Mathematical Bulletin
• Print ISSN: 0008-4395
• Electronic ISSN: 1496-4287
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 68
• Issue: 2
• Pages: 492-511
• DOI: https://doi.org/10.4153/S0008439524000778
• Public URL: https://durham-repository.worktribe.com/output/3105805