We study the lower bound for Koldobsky’s slicing inequality. We show that there exists a measure μ and a symmetric convex body Kn, such that for all (Formula Presented) and all t,μ+(K∩(ξ⊥+tξ))≤cnμ(K)|K|−1n. Our bound is optimal, up to the value of the universal constant. It improves slightly upon the results of the first named author and Koldobsky, which included a doubly-logarithmic error. The proof is based on an efficient way of discretizing the unit sphere.
|Title of host publication||Lecture Notes in Mathematics|
|Number of pages||21|
|State||Published - 2020|
|Name||Lecture Notes in Mathematics|
- Convex bodies