Quantitative form of Ball's Cube slicing in $\mathbb{R}^n$ and equality cases in the min-entropy power inequality

James Melbourne; Cyril Roberto

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arXiv · 2109.03946

Quantitative form of Ball's Cube slicing in $\mathbb{R}^n$ and equality cases in the min-entropy power inequality

James Melbourne·Cyril Roberto

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Abstract

We prove a quantitative form of the celebrated Ball's theorem on cube slicing in $\mathbb{R}^n$ and obtain, as a consequence, equality cases in the min-entropy power inequality. Independently, we also give a quantitative form of Khintchine's inequality in the special case $p=1$.

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James Melbourne, Cyril Roberto. 2021-09-08. Quantitative form of Ball's Cube slicing in $\mathbb{R}^n$ and equality cases in the min-entropy power inequality. https://arxiv.org/abs/2109.03946

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