2018/03/31 by Vitor Balestro, Balestro, Vitor, Horst Martini +1
Mathematics · #52A10 #52A21 #52A40 #53A35 #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1804.00215
openalex publication_date 2018/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We aim to study the classical Rosenthal-Szasz inequality for a plane whose geometry is given by a norm. This inequality states that the bodies of constant width have the largest perimeter among all planar convex bodies of given diameter. In the case where the unit circle of the norm is given by a Radon curve, we obtain an inequality which is completely analogous to the Euclidean case. For arbitrary norms we obtain an upper bound for the perimeter calculated in the anti-norm, yielding an analogous characterization of all curves of constant width. To derive these results, we use methods from the differential geometry of curves in normed planes.