Extremal problems for spherical convex polygons

DOI10.1007/s00013-021-01698-7zbMath1487.52016OpenAlexW4211068077MaRDI QIDQ2131246

Cen Liu, Yan Xun Chang

Publication date: 25 April 2022

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-021-01698-7

zbMATH Keywords

areathicknessperimeterspherical polygonisodiametric

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Spherical and hyperbolic convexity (52A55)

Cites Work

• Enumerating isodiametric and isoperimetric polygons
• A discrete isoperimetric problem
• The small octagon with longest perimeter
• Isoperimetric polygons of maximum width
• The largest small hexagon
• Barbier's theorem for the sphere and the hyperbolic plane
• On convex polygons of maximal width
• Using symbolic calculations to determine largest small polygons
• Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes
• The perimeter and area of reduced spherical polygons of thickness \(\pi /2\)
• The isodiametric problem on the sphere and in the hyperbolic space
• Width of spherical convex bodies
• Extremal problems for convex polygons
• Isodiametric problems for polygons
• A $1 Problem
• The Isoperimetric Problem
• Reduced spherical polygons

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