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

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 \(2\).

arXiv comment27 pages