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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 Lp-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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BibTeX
@misc{fan2026sharp,
title = {{Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part II: The Case $1<p<2$}},
author = {Song Fan and Gui-Dong Li and Jianjun Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28215},
eprint = {2609.28215},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28215},
}
RIS
TY - UNPB
TI - Sharp Quantitative Stability for the Affine p-Sobolev Inequality, Part II: The Case 1<p<2
AU - Song Fan
AU - Gui-Dong Li
AU - Jianjun Zhang
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28215
UR - https://arxiv.org/abs/2609.28215
AB - 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.
ER -