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arXiv · 2609.28215

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part II: The Case $1<p<2$

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 \(1<p<2\), 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 \(2\).

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Song Fan, Gui-Dong Li, Jianjun Zhang. 2026-09-23. Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part II: The Case $1<p<2$. https://arxiv.org/abs/2609.28215

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