Spherical Geometry—A Survey on Width and Thickness of Convex Bodies

DOI10.1007/978-3-030-86695-2_2zbMath1502.52012arXiv2012.13652OpenAlexW4213260742MaRDI QIDQ5050923

Marek Lassak

Publication date: 18 November 2022

Published in: Surveys in Geometry I (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.13652

zbMATH Keywords

areaextreme pointthicknessconvex polygonwidthspherical geometrydiameterconvex bodyconstant widthperimeterhemispherereduced bodycomplete bodyluneconstant diameter

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Spherical and hyperbolic convexity (52A55) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Research exposition (monographs, survey articles) pertaining to convex and discrete geometry (52-02) Plane and spherical trigonometry (educational aspects) (97G60)

Related Items (5)

Complete sets in normed linear spaces ⋮ On a strengthening of the Blaschke-Leichtweiss theorem ⋮ Stability of the isodiametric problem on the sphere and in the hyperbolic space ⋮ Covering a reduced spherical polygon by a disk ⋮ Width of convex bodies in hyperbolic space

Cites Work

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• The isodiametric problem and other inequalities in the constant curvature 2-spaces
• Measures of symmetry for convex sets and stability
• Geometric probability on the sphere
• Reduced convex bodies in Euclidean space -- a survey
• Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width
• Ausgewählte Probleme der kombinatorischen Geometrie des Euklidischen und sphärischen Raumes
• Reduced convex bodies in the plane
• Width of convex bodies in spaces of constant curvature
• Extremal convex sets
• Convex hulls and extreme points of some families of multivalent functions
• Barbier's theorem for the sphere and the hyperbolic plane
• On the smallest disk containing a planar reduced convex body
• Spherical bodies of constant width
• Self-dual Wulff shapes and spherical convex bodies of constant width \({\pi}/{2}\)
• Completeness and constant width in spherical and hyperbolic spaces
• The Jung theorem for spherical and hyperbolic spaces
• Constant width and transnormality in spheres
• Hunting for reduced polytopes
• Covering of a reduced spherical body by a disk
• Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes
• From spherical to Euclidean illumination
• Complete spherical convex bodies
• The perimeter and area of reduced spherical polygons of thickness \(\pi /2\)
• Constant diameter and constant width of spherical convex bodies
• Reduced convex bodies in finite dimensional normed spaces: a survey
• The isodiametric problem on the sphere and in the hyperbolic space
• When is a spherical body of constant diameter of constant width?
• Width of spherical convex bodies
• Projections onto convex sets on the sphere
• Reduced bodies in normed planes
• A spherical Hellytype theorem
• Curves of constant width in the non-Euclidean geometry
• Convex regions on the \(n\)-dimensional spherical surface
• Binary operations in spherical convex geometry
• On the works of Euler and his followers on spherical geometry
• Über eine Übertragung des Hellyschen Satzes in Sphärische Räume
• Reduced spherical convex bodies
• Bodies of Constant Width
• Heavenly Mathematics
• Three Theorems of Menelaus
• Convexity theory on spherical spaces (I)
• Spherical Geometry and Its Applications
• Reduced spherical polygons
• Note on convex spherical curves
• Kleine Studie zur Kombinatorischen Geometrie der Sphäre
• Metric spaces, convexity and nonpositive curvature

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