Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$

Song Fan; Gui-Dong Li; Jianjun Zhang

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arXiv · 2606.09555

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$

Song Fan·Gui-Dong Li·Jianjun Zhang

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Abstract

We prove a sharp quantitative stability result for the affine $L^p$-Sobolev inequality, for $p\ge2$, introduced by Lutwak--Yang--Zhang (\emph{J. Differential Geom.}, \textbf{62} (2002), 17--38). Moreover, the stability exponent is shown to be optimal, and equal to $p$.

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Song Fan, Gui-Dong Li, Jianjun Zhang. 2026-06-08. Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$. https://arxiv.org/abs/2606.09555

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