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Estimates for moments of general measures on convex bodies

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arxiv 1712.05949 v1 pith:BBLHZEAZ submitted 2017-12-16 math.MG

Sergey Bobkov , Bo'az Klartag , Alexander Koldobsky This is my paper · ORCID
classification math.MG
keywords convexestimatesbodiesmeasuresmomentsarbitraryproveapply
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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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  1. Isomorphic Busemann--Petty for arbitrary measures: the sharp order

    math.FA 2026-08 conditional novelty 7.0 of 10

    The optimal constant in the isomorphic Busemann-Petty problem for arbitrary even densities has the sharp order √n: a new lower bound C_n ≥ c√n matches the known upper bound C_n ≤ √n.

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