The effect of dimension four in Aleksandrov's problem of filling a space by polyhedra

DOI10.1007/BF00129910zbMath0573.52024MaRDI QIDQ1063254

Boris N. Apanasov

Publication date: 1986

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

zbMATH Keywords

complete hyperbolic orbifoldsincomplete hyperbolic orbifoldsproblem of Aleksandrovrigidity of deformations of hyperbolic orbifoldstiling the hyperbolic space by polyhedra

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Deformations of general structures on manifolds (58H15) Discrete subgroups of Lie groups (22E40) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Combinatorial aspects of tessellation and tiling problems (05B45) Deformations of analytic structures (32G99)

Related Items (4)

The geometry of Nielsen's hull for a Kleinian group in space and quasi- conformal mappings ⋮ Bending and stamping deformations of hyperbolic manifolds ⋮ Polyhedron complexes with simply transitive group actions and their realizations ⋮ Nonstandard uniformized conformal structures on hyperbolic manifolds

Cites Work

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• Geometrically finite hyperbolic structures on manifolds
• On a remarkable class of polyhedra in complex hyperbolic space
• Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
• Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups
• Sur les polygones générateurs de groupes fuchsiens
• On Poincaré's theorem for fundamental polygons
• Conformally Flat Manifolds with Nilpotent Holonomy and the Uniformization Problem for 3-Manifolds
• On discontinuous groups acting on a real hyperbolic space, I

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