2025/05/29 by Shay Sadovsky, Gaoyong Zhang, Sadovsky, Shay +1
Computer Science · Mathematics · #52A40 #Computational Geometry and Mesh Generation #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Morphological variations and asymmetry #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2505.23748
openalex publication_date 2025/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper establishes two new geometric inequalities in the dual Brunn-Minkowski theory. The first, originally conjectured by Lutwak, is the Brunn-Minkowski inequality for dual quermassintegrals of origin-symmetric convex bodies. The second, generalizing Ball's volume ratio inequality, is a reverse isoperimetric inequality: among all origin-symmetric convex bodies in John's position, the cube maximizes the dual quermassintegrals.