Calculus of Variations and Geometric Measure Theory

R. Gasteldello - A. Henrot - I. Lucardesi

About the Blaschke-Santalo diagram of area, perimeter and moment of inertia

created by lucardesi on 21 Jul 2023
modified on 31 Jan 2024


Accepted Paper

Inserted: 21 jul 2023
Last Updated: 31 jan 2024

Journal: Journal of Convex Analysis
Year: 2024


We study the Blaschke-Santal´o diagram associated to the area, the perimeter, and the moment of inertia. We work in dimension 2, under two assumptions on the shapes: convexity and the presence of two orthogonal axis of symmetry. We discuss topological and geometrical properties of the diagram. As a by-product we address a conjecture by P´olya, in the simplified setting of double symmetry.