Filling a space by polyhedra and deformation of incomplete hyperbolic structures
type: Item
instance of: scholarly article
title: Filling a space by polyhedra and deformation of incomplete hyperbolic structures
zbMATH Open document ID: 0667.57025
DOI: 10.1007/BF00969160
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The author obtains conditions for complete filling of hyperbolic spaces by unbounded polyhedra with finite numbers of sides for dimensions \(n\leq 3\), and finite volumes for dimensions \(n\geq 4\). In dimensions \(n\leq 3\) these conditions are the conditions in A. D. Aleksandrov's theorem for complete filling of hyperbolic spaces by bounded polyhedra, together with the local finiteness condition for the filling. In dimensions \(n\geq 4\) these conditions for unbounded polyhedra topologically similar to polyhedra with a complete filling are the same as the conditions in the Aleksandrov theorem. These results could be considered as generalizations of the classical Poincaré theorems about fundamental polygons and polyhedra. The methods used in this paper are closely connected to the study of the deformations of complete and incomplete hyperbolic manifolds and orbifolds. A strong rigidity for such manifolds in dimensions \(n\geq 4\) is obtained.
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 57Q99
Mathematics Subject Classification ID: 57M99
zbMATH DE Number: 4092372
zbMATH Keywords: filling of hyperbolic spaces by unbounded polyhedra
zbMATH Keywords: deformations of complete and incomplete hyperbolic manifolds and orbifolds
zbMATH Keywords: strong rigidity
author: Boris N. Apanasov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4092372