ON THE MAXIMIZATION OF A CLASS OF FUNCTIONALS ON CONVEX REGIONS, AND THE CHARACTERIZATION OF THE FARTHEST CONVEX SET

DOI10.1112/S0025579310000495zbMath1202.52001arXiv0905.1464OpenAlexW2155377230MaRDI QIDQ3584590

Antoine Henrot, Evans M. II. Harrell

Publication date: 30 August 2010

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.1464

zbMATH Keywords

Hausdorff distance\(L^2\) distanceplanar convex set

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Optimization of shapes other than minimal surfaces (49Q10) Isoperimetric problems for polytopes (52B60) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (2)

Semidefinite programming for optimizing convex bodies under width constraints ⋮ On the inverse spectral problem for Euclidean triangles

Cites Work

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• On the critical exponent in an isoperimetric inequality for chords
• Polygonal approximation of plane convex bodies
• Inequalities for means of chords, with application to isoperimetric problems
• Variation and optimization of formes. A geometric analysis
• Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions
• Polygons as Optimal Shapes with Convexity Constraint
• The Hausdorff distance between compact convex sets
• First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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