Discreteness and Convergence of Complex Hyperbolic Isometry Groups

Abstract and Applied Analysis ◽

10.1155/2013/638638 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5

Author(s):

Xi Fu

Keyword(s):

Isometry Groups ◽

Convergence Theorems ◽

Discreteness Criteria ◽

Algebraic Convergence

We investigate the discreteness and convergence of complex isometry groups and some discreteness criteria and algebraic convergence theorems for subgroups ofPU(n,1)are obtained. All of the results are generalizations of the corresponding known ones.

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Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups

Abstract and Applied Analysis ◽

10.1155/2014/684594 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5

Author(s):

Huani Qin ◽

Yueping Jiang ◽

Wensheng Cao

Keyword(s):

Hyperbolic Space ◽

Convergence Theorem ◽

Kleinian Group ◽

Isometry Groups ◽

Quaternionic Hyperbolic Space ◽

Algebraic Convergence ◽

Real Hyperbolic Space ◽

Jørgensen’S Inequality ◽

Algebraic Limit

We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if ther-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group. Our results are generalizations of the counterparts in then-dimensional real hyperbolic space.

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Algebraic convergence theorems of n-dimensional Kleinian groups

Israel Journal of Mathematics ◽

10.1007/s11856-007-0096-5 ◽

2007 ◽

Vol 162 (1) ◽

pp. 221-233 ◽

Cited By ~ 7

Author(s):

Xiantao Wang

Keyword(s):

Kleinian Groups ◽

Convergence Theorems ◽

Algebraic Convergence

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ALGEBRAIC CONVERGENCE THEOREMS OF COMPLEX KLEINIAN GROUPS

Glasgow Mathematical Journal ◽

10.1017/s0017089512000304 ◽

2012 ◽

Vol 55 (1) ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

WENSHENG CAO

Keyword(s):

Kleinian Groups ◽

Limit Group ◽

Convergence Theorems ◽

Möbius Group ◽

Algebraic Convergence ◽

Algebraic Limit

AbstractLet {Gr,i} be a sequence of r-generator subgroups of U(1,n; ℂ) and Gr be its algebraic limit group. In this paper, two algebraic convergence theorems concerning {Gr,i} and Gr are obtained. Our results are generalisations of their counterparts in the n-dimensional sense-preserving Möbius group.

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