Cone-volume measures of polytopes

2013/05/23 by Henk, Martin, Linke, Eva · 1 citation
#52A40 #52B11 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1305.5335

Abstract

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.

Cited by

• On polynomial inequalities for cone-volumes of polytopes

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• Cone-volume measure and stability
• Affine Subspace Concentration Conditions for Centered Polytopes
• On polynomial inequalities for cone-volumes of polytopes
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• The affine subspace concentration inequality for centered convex bodies