Blaschke-Santalo Diagrams of Planar Convex Sets via Shape Optimization
A method that couples theoretical results with numerical shape optimization to produce improved, near-rigorous descriptions of Blaschke-Santalo diagrams - the regions capturing every inequality among a triplet of shape functionals over planar convex bodies. It proves the diagrams for (perimeter, diameter, area) and the new (diameter, first Dirichlet eigenvalue, area) triplet lie between continuous monotone extremal functions, introduces a radial-function parametrization casting convexity as quadratic inequality constraints, and uncovers a non-continuity of extremal shapes in the diameter-eigenvalue diagram.
Improved description of Blaschke–Santaló diagrams via numerical shape optimization Ilias Ftouhi
A mathematics (math.OC) research paper combining theoretical proofs with numerical shape optimization to obtain sharper descriptions of Blaschke-Santalo diagrams for planar convex bodies. A Blaschke-…