The effect of dimension 4 in Aleksandrov's problem of filling a space by polyhedra

✍ Scribed by B. N. Apanasov

• Publisher: Springer
• Year: 1986
• Tongue: English
• Weight: 715 KB
• Volume: 4
• Category: Article
• ISSN: 0232-704X
• DOI: 10.1007/bf00129910

✦ Synopsis

This paper deals with filling the hyperbolic space H n by noncompact polyhedra. In dimensions n 4 the non-compact case is very different from the compact one, which was investigated by A.D.Aleksandrov. For n 4 the compact and non-compact cases are "almost" similar. This investigation is closely related to deformations of complete and incomplete hyperbolic orbifolds (in the sense of W.Thurston) for which a strong rigidity result is proved -similar to the one for complete hyperbolic manifolds in dimension exceeding two.