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arXiv · 1712.05949

Estimates for moments of general measures on convex bodies

Sergey Bobkov·Bo'az Klartag·Alexander Koldobsky
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Abstract

We prove several estimates for the moments of arbitrary measures on convex bodies. We apply these estimates to show a new slicing inequality for measures on convex bodies. We also deduce estimates for the outer volume ratio distance from an arbitrary centrally-symmetric convex body in R^n to the class of unit balls of n-dimensional subspaces of L_p-spaces. Finally, we prove a result of the Busemann-Petty type for these moments.

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Sergey Bobkov, Bo'az Klartag, Alexander Koldobsky. 2017-12-16. Estimates for moments of general measures on convex bodies. https://arxiv.org/abs/1712.05949

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