A hyperplane inequality for measures of convex bodies in $\R^n,\ n\le 4$

Details A hyperplane inequality for measures of convex bodies in $\R^n,\ n\le 4$ A hyperplane inequality for measures of convex bodies in $\R^n,\ n\le 4$

2011-02-20

arxiv.org/abs/1102.4081v1

Mathematics

Metric Geometry

Scientific paper

We generalize the hyperplane inequality in dimensions up to 4 to the setting of arbitrary measures in place of the volume. To prove this generalization we establish stability in the affirmative part of the solution to the Busemann-Petty problem asking whether symmetric convex bodies in R^n with smaller (n-1)-dimensional volume of all central hyperplane sections necessarily have smaller n-dimensional volume.

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