Affinely regular polygons as extremals of area functionals

DOI10.1007/s00454-007-9010-5zbMath1155.52001OpenAlexW1963549572MaRDI QIDQ2482187

Marco Longinetti, Paolo Gronchi

Publication date: 16 April 2008

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-007-9010-5

zbMATH Keywords

geometric tomographyaffine lengthaffinely regular polygon

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (4)

Volume Frameworks and Deformation Varieties ⋮ A characterization of affinely regular polygons ⋮ On the volume of the convex hull of two convex bodies ⋮ Affine properties of convex equal-area polygons

Cites Work

• Reconstructing plane sets from projections
• An isoperimetric inequality for convex polygons and convex sets with the same symmetrals
• Affine regularity
• Properties of affinely regular polygons
• A maximum property of affinely regular polygons
• A characterization of affine length and asymptotic approximation of convex discs
• On the geometric structure of lattice \(U\)-polygons
• Dropping a vertex or a facet from a convex polytope
• On Hammer's X-Ray Problem
• Some questions of stability in the reconstruction of plane convex bodies from projections
• Polygons Whose Vertex Triangles Have Equal Area
• EFFICIENT APPROXIMATION OF CONVEX POLYGONS
• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]
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