Sharp stability on the second Robin eigenvalue with negative boundary parameters
Analysis of PDEs
2025-12-05 v1
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.
Cite
@article{arxiv.2512.04584,
title = {Sharp stability on the second Robin eigenvalue with negative boundary parameters},
author = {Zhijie Chen and Zhen Song and Wenming Zou},
journal= {arXiv preprint arXiv:2512.04584},
year = {2025}
}