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.
Bourgain,On high-dimensional maximal functions associated to convex bodies, Amer
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Isomorphic Busemann--Petty for arbitrary measures: the sharp order
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.