The isodiametric problem and other inequalities in the constant curvature 2-spaces

DOI10.1007/s13398-014-0183-5zbMath1325.52007OpenAlexW2079640348MaRDI QIDQ496366

María A. Hernández Cifre, Antonio R. Martínez Fernández

Publication date: 21 September 2015

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-014-0183-5

zbMATH Keywords

areadiameterperimeterminimal (geodesic) widthRosenthal-Szasz theoremspherical/hyperbolic isodiametric inequalityspherical/hyperbolic symmetric convex bodies

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Spherical and hyperbolic convexity (52A55) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (4)

Spherical Geometry—A Survey on Width and Thickness of Convex Bodies ⋮ Stability of the isodiametric problem on the sphere and in the hyperbolic space ⋮ THE ROSENTHAL–SZASZ INEQUALITY FOR NORMED PLANES ⋮ On the isodiametric and isominwidth inequalities for planar bisections

Cites Work

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• Integral geometry and geometric inequalities in hyperbolic space
• Width of convex bodies in spaces of constant curvature
• Asymptotic behavior of convex sets in the hyperbolic plane
• Geometry of surfaces
• The Jung theorem for spherical and hyperbolic spaces
• Bonnesen-type inequalities for surfaces of constant curvature
• Über die isoperimetrische Aufgabe im \(n\)-dimensionalen Raum konstanter negativer Krümmung. I: Die isoperimetrische \(n\) Ungleichungen in der hyperbolischen Ebene und für Rotationskörper im \(n\)-dimensionalen hyperbolischen Raum
• Perimeter, Diameter and Area of Convex Sets in the Hyperbolic Plane

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