A $sqrt{n}$ estimate for measures of hyperplane sections of convex bodies

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arxiv 1309.5271 v1 pith:PRGVYNTN submitted 2013-09-20 math.MG

Alexander Koldobsky This is my paper · ORCID

classification math.MG

keywords bodiesconvexestimatesectionsarbitraryhyperplaneintersectionmeasure

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We prove an estimate for arbitrary measure of sections of convex bodies. The proof is based on a stability result for intersection bodies.

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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.