Work

Improved Description of Blaschke–Santaló Diagrams via Numerical Shape Optimization

Year: 2025

Type: article

Abstract: We propose a method based on the combination of theoretical results on Blaschke–Santaló diagrams and numerical shape optimization techniques to obtain improved description of Blaschke–Santaló diagrams in the class of planar convex sets. To illustrate our approach, we study three relevant diagrams involving the perimeter P, the diameter d, the area A and the first eigenvalue of the Laplace operator with Dirichlet boundary condition $$\lambda _1$$ λ 1 . The first diagram is a purely geometric one involving the triplet (P, d, A) and the two other diagrams involve geometric and spectral functionals, namely $$(P,\lambda _1,A)$$ ( P , λ 1 , A ) and $$(d,\lambda _1,A)$$ ( d , λ 1 , A ) where a strange phenomenon of non-continuity of the extremal shapes is observed.

Source: Applied Mathematics & Optimization

DOI: 10.1007/s00245-025-10250-w

Author: Ilias Ftouhi

Institutions: King Fahd University of Petroleum and Minerals, Friedrich-Alexander-Universität Erlangen-Nürnberg

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,890

Funders: Alexander von Humboldt-Stiftung, Friedrich-Alexander-Universität Erlangen-Nürnberg, Agence Nationale de la Recherche