Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind

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• 作者：Lior Fishman ; David Simmons ; Mariusz Urbański
• 关键词：Hyperbolic space ; Kleinian groups ; Limit sets ; Rigidity
• 刊名：Geometriae Dedicata
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：178
• 期：1
• 页码：95-101
• 全文大小：384 KB
• 参考文献：1.Bowditch, B.H.: Geometrical finiteness for hyperbolic groups. J. Funct. Anal. 113(2), 245-17 (1993)MATH MathSciNet CrossRef
  2.Burger, M., Iozzi, A., Monod, N.: Equivariant embeddings of trees into hyperbolic spaces. Int. Math. Res. Not. (22), 1331-369 (2005)
  3.Das, T., Simmons, D.S., Urbański, M.: Geometry and Dynamics in Gromov Hyperbolic Metric Spaces I: With an Emphasis on Non-proper Settings. arXiv:-409.-155 , preprint (2014)
  4.Greenberg, L.: Discrete groups of motions. Can. J. Math. 12, 415-26 (1960)MATH CrossRef
  5.Greenberg, L.: Discrete subgroups of the Lorentz group. Math. Scand. 10, 85-07 (1962)MATH MathSciNet
  6.Susskind, P., Swarup, G.A.: Limit sets of geometrically finite hyperbolic groups. Am. J. Math. 114(2), 233-50 (1992)MATH MathSciNet CrossRef
  7.Yang, W.-Y., Jiang, Y.-P.: Limit sets and commensurability of Kleinian groups. Bull. Aust. Math. Soc. 82(1), 1- (2010)MATH MathSciNet CrossRef
  
• 作者单位：Lior Fishman (1)
  David Simmons (2)
  Mariusz Urbański (1)
  
  1. Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX, 76203-5017, USA
  2. Department of Mathematics, Ohio State University, 231 W. 18th Avenue, Columbus, OH, 43210-1174, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9168

文摘

We consider the relation between geometrically finite groups and their limit sets in infinite-dimensional hyperbolic space. Specifically, we show that a rigidity theorem of Susskind and Swarup (Am J Math 114(2):233-50, 1992) generalizes to infinite dimensions, while a stronger rigidity theorem of Yang and Jiang (Bull Aust Math Soc 82(1):1-, 2010) does not. Keywords Hyperbolic space Kleinian groups Limit sets Rigidity