2014/11/14 by Károly J. Böröczky, Böröczky, K. J., Endre Makai +1
Mathematics · #52A10 #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary: 52A40 #Secondary: 52A38
paper · pdf · doi:10.48550/arxiv.1411.3842
openalex publication_date 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the Blaschke-Santaló inequality restricted to n-gons: the extremal polygons are the affine regular n-gons. If either the John or the Löwner ellipse of a planar o-symmetric convex body K is the unit circle about o, then a sharpening of the Blaschke-Santaló inequality holds: even the aritmetic mean ( V(K) + V( K^*) ) /2 is at least π. We give stability variants of the Blaschke-Santaló inequality for the plane. If for some n ≥ 3 the planar convex body K is n-fold rotationally symmetric about o, then we give the exact maximum of V(K^*), as a function of V(K) and the area of either the John or the Löwner ellipse.