Year: 2026
Type: preprint
Abstract: We establish sharp quantitative stability estimates for the Hong--Krahn--Szegő inequality for arbitrary open sets of positive finite measure in $\mathbb R^d$, $d\ge2$. In dimensions $d\ge3$, the optimal stability exponent is $(d+2)/2$, while in dimension two the sharp stability modulus is $t^2/\log(e/t)$. These results improve the quantitative stability estimate of Brasco and Pratelli~\cite[Theorem 3.5]{BP} and resolve Open Problem 7.56 of Brasco and De Philippis~\cite[Open Problem 7.56]{BDP}.
Source: arXiv (Cornell University)
Authors: Zhou, Yuxuan, Zou, Wenming
Institution: Tsinghua University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8593688678
OpenAlex ID: W7223247994