Theoretical analysis demonstrates dimension-free stability of simplex slicing in convex bodies, indicating universal bounds for section volumes across dimensions.
We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary convex bodies. We prove that isotropic bodies enjoy it with a universal constant.
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Myroshnychenko et al. (2024) studied this question.
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