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math.AP2024
The Weighted Minkowski Problem
Dylan Langharst, Jiaqian Liu, Shengyu Tang
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex…
math.MG2024
Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions
Dylan Langharst, Francisco Marín Sola, Jacopo Ulivelli
The Rogers-Shephard and Zhang's projection inequalities are two reverse, affine isoperimetric-type inequalities for convex bodies. Following a classical work by Schneider, both ine…