zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Discreteness and convergence of Möbius groups. (English) Zbl 1053.30038
In this paper, the author shows that a fixed nontrivial Möbius transformation can be used as a test map to test the discreteness of a nonelementary Möbius group. Following Jorgensen’s well-known result about the discreteness of a group of Möbius transformations, the author proves two discreteness theorems. The first of these two results says that if for every element g of an n-dimensional subgroup $G$ of I$som(Hn)$, the group $<g,h>$ is discrete , then $G$ is discrete. The second discreteness theorem states some conditions for the discreteness of G. Also two convergence theorems are given at the end.

30F40Kleinian groups
28A78Hausdorff and packing measures
Full Text: DOI