Isoperimetric Inequalities in Normed Planes

zbMath1487.52015arXiv2008.12801MaRDI QIDQ5074504

Rafael S. dos Santos, Marcos Craizer

Publication date: 9 May 2022

Full work available at URL: https://arxiv.org/abs/2008.12801

zbMATH Keywords

isoperimetric inequalitiesMinkowski geometryWigner causticnormed planecurves of constant width

Mathematics Subject Classification ID

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

Cites Work

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• The improved isoperimetric inequality and the Wigner caustic of planar ovals
• Iteration of involutes of constant width curves in the Minkowski plane
• Semi-inner products and the concept of semi-polarity
• Duality of gauges and symplectic forms in vector spaces
• On isoperimetric inequalities in Minkowski spaces
• On plane Minkowski geometry
• Closed cycloids in a normed plane
• On Legendre curves in normed planes
• Discrete cycloids from convex symmetric polygons
• Concepts of curvatures in normed planes
• Antinorms and Radon curves
• Involutes of polygons of constant width in Minkowski planes
• The Isoperimetric Problem in the Minkowski Plane
• THE ROSENTHAL–SZASZ INEQUALITY FOR NORMED PLANES
• Maximum area with Minkowski measures of perimeter
• The Isoperimetric Problem in the Minkowski Plane

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