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arXiv · 2512.04584

Sharp stability on the second Robin eigenvalue with negative boundary parameters

Zhijie Chen·Zhen Song·Wenming Zou
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Abstract

In this paper, we prove a quantitative refinement of the isoperimetric type inequality for the second Robin eigenvalue with negative boundary parameters established by Freitas and Laugesen [Amer.J.Math.143 (2021), no.3, 969-994].Such new stability estimate is proved when the boundary parameter is not too far from 0.By constructing a suitable family of nearly spherical domains, we prove that the exponent for the Fraenkel asymmetry in this quantitative type inequality is sharp.

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Zhijie Chen, Zhen Song, Wenming Zou. 2025-12-04. Sharp stability on the second Robin eigenvalue with negative boundary parameters. https://arxiv.org/abs/2512.04584

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