We study the Blaschke-Santalo 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 Polya, in the simplified setting of double symmetry.
About the Blaschke-Santaló Diagram of Area, Perimeter and Moment of Inertia
Lucardesi I.
2024-01-01
Abstract
We study the Blaschke-Santalo 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 Polya, in the simplified setting of double symmetry.File in questo prodotto:
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