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

Lior Fishman; David Simmons; Mariusz Urbański

doi:10.1007/s10711-015-0045-0

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

Lior Fishman
, David Simmons
, Mariusz Urbański

Research output: Contribution to journal › Article › peer-review

Abstract

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):233–250, 1992) generalizes to infinite dimensions, while a stronger rigidity theorem of Yang and Jiang (Bull Aust Math Soc 82(1):1–9, 2010) does not.

Original language	English
Pages (from-to)	95-101
Number of pages	7
Journal	Geometriae Dedicata
Volume	178
Issue number	1
DOIs	https://doi.org/10.1007/s10711-015-0045-0
State	Published - 24 Oct 2015
Externally published	Yes

Keywords

Hyperbolic space
Kleinian groups
Limit sets
Rigidity

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-015-0045-0

Cite this

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abstract = "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):233–250, 1992) generalizes to infinite dimensions, while a stronger rigidity theorem of Yang and Jiang (Bull Aust Math Soc 82(1):1–9, 2010) does not.",

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N2 - 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):233–250, 1992) generalizes to infinite dimensions, while a stronger rigidity theorem of Yang and Jiang (Bull Aust Math Soc 82(1):1–9, 2010) does not.

AB - 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):233–250, 1992) generalizes to infinite dimensions, while a stronger rigidity theorem of Yang and Jiang (Bull Aust Math Soc 82(1):1–9, 2010) does not.

KW - Hyperbolic space

KW - Kleinian groups

KW - Limit sets

KW - Rigidity

UR - https://www.scopus.com/pages/publications/84942192045

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

Abstract

Keywords

ASJC Scopus subject areas

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