Stability in the Busemann-petty and Shephard Problems
نویسنده
چکیده
A comparison problem for volumes of convex bodies asks whether inequalities fK(ξ) ≤ fL(ξ) for all ξ ∈ S imply that Voln(K) ≤ Voln(L), where K,L are convex bodies in R, and fK is a certain geometric characteristic of K. By linear stability in comparison problems we mean that there exists a constant c such that for every ε > 0, the inequalities fK(ξ) ≤ fL(ξ) + ε for all ξ ∈ S imply that (Voln(K)) n−1
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