Small deformations of polygons and polyhedra

DOI10.1090/S0002-9947-06-04172-9zbMath1126.53041arXivmath/0410058OpenAlexW2164667412MaRDI QIDQ3420396

Jean-Marc Schlenker

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410058

zbMATH Keywords

polyhedrapolygonisoperimetric property for hyperbolic polygonsrigidity for polyhedral surfaces in Minkowski spacevariations of angles

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Inequalities and extremum problems in real or complex geometry (51M16)

Related Items (15)

The geometry of cyclic hyperbolic polygons ⋮ Fuchsian convex bodies: basics of Brunn-Minkowski theory ⋮ Rigidity of bordered polyhedral surfaces ⋮ Calculus of generalized hyperbolic tetrahedra ⋮ Regenerating hyperbolic cone 3-manifolds from dimension 2 ⋮ Flippable tilings of constant curvature surfaces ⋮ Hyperbolic polygons of minimal perimeter with given angles ⋮ Polyhedral hyperbolic metrics on surfaces ⋮ Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes ⋮ Circle patterns on singular surfaces ⋮ Infinitesimal conformal deformations of triangulated surfaces in space ⋮ Fuchsian polyhedra in Lorentzian space-forms ⋮ On the infinitesimal rigidity of weakly convex polyhedra ⋮ A Variational Principle for Cyclic Polygons with Prescribed Edge Lengths ⋮ The centered dual and the maximal injectivity radius of hyperbolic surfaces

Cites Work

• Convex polyhedra in Lorentzian space-forms
• Ungleichungen über konvexe Polyeder
• Infinitesimal rigidity of almost-convex oriented polyhedra of arbitrary Euler characteristic
• Rigidity and the Alexandrov-Fenchel inequality
• A characterization of compact convex polyhedra in hyperbolic 3-space
• Metrics on hyperbolic convex polyhedra
• Flexible polyhedra in Minkowski 3-space
• A Dido problem as modernized by Fejes Tóth
• Convex Fuchs surfaces in Lorentz spaces of constant curvature
• On the Moduli Space of a Spherical Polygonal Linkage
• A Geometrical Background for De Sitter's World
• On the moduli space of polygons in the Euclidean plane
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