A hyperplane inequality for measures of convex bodies in ⁿ,n≤ 4

Original · EN

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 Rⁿ with smaller (n-1)-dimensional volume of all central hyperplane sections necessarily have smaller n-dimensional volume.