Abstract

We study the Blaschke-Santaló 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 axes of symmetry. We discuss topological and geometrical properties of the diagram. As a by-product we address a conjecture by Pólya, in the simplified setting of double symmetry.

Author information

Contact details are reproduced from the original publication and may be historical.

Ilaria Lucardesi

(1) Dip. di Matematica e Informatica "Ulisse Dini", University of Florence, Italy
(2) Dip. di Matematica, University of Pisa, Pisa, Italy

ilaria.lucardesi@unipi.it

Keywords

  • Shape optimization
  • area
  • perimeter
  • moment of inertia
  • convex geometry
  • Blaschke-Santaló diagram

Mathematics Subject Classification

49Q10, 52A40, 28A75

Suggested citation

R. Gastaldello, A. Henrot, I. Lucardesi. “About the Blaschke-Santaló Diagram of Area, Perimeter and Moment of Inertia.” Journal of Convex Analysis 31 (2024), No. 2, 563–602.

Copyright Heldermann Verlag 2024