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

09/08/2021

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by   James Melbourne, et al.

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We prove a quantitative form of the celebrated Ball's theorem on cube slicing in 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.