Cone-volume measures of polytopes
classification
🧮 math.MG
math.DG
keywords
cone-volumeaffinealongcentroidcompletelyconcentrationconditionconditions
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The cone-volume measure of a polytope with centroid at the origin is proved to satisfy the subspace concentration condition. As a consequence a conjectured (a dozen years ago) fundamental sharp affine isoperimetric inequality for the U-functional is completely established -- along with its equality conditions.
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