Consequences of the action of the Cremona group of an infinite dimensional hyperbolic space

2021 ◽  
pp. 131-158
Keyword(s):  
Hyperbolic Space ◽  
Cremona Group ◽  
Infinite Dimensional

scholarly journals Kähler groups, real hyperbolic spaces and the Cremona group. With an appendix by Serge Cantat

2011 ◽  
Vol 148 (1) ◽  
pp. 153-184 ◽  
Author(s):  
Thomas Delzant ◽  
Pierre Py
Keyword(s):  
Hyperbolic Space ◽  
Discrete Subgroup ◽  
Hyperbolic Spaces ◽  
Classical Theorem ◽  
Isometric Action ◽  
Cremona Group ◽  
The Real ◽  
Infinite Dimensional ◽  
Kähler Groups ◽  
Real Hyperbolic Space

AbstractGeneralizing a classical theorem of Carlson and Toledo, we prove thatanyZariski dense isometric action of a Kähler group on the real hyperbolic space of dimension at least three factors through a homomorphism onto a cocompact discrete subgroup of PSL2(ℝ). We also study actions of Kähler groups on infinite-dimensional real hyperbolic spaces, describe some exotic actions of PSL2(ℝ) on these spaces, and give an application to the study of the Cremona group.

The Bishop–Jones relation and Hausdorff geometry of convex-cobounded limit sets in infinite-dimensional hyperbolic space

2016 ◽  
Vol 16 (05) ◽  
pp. 1650018 ◽  
Author(s):  
Tushar Das ◽  
Bernd O. Stratmann ◽  
Mariusz Urbański
Keyword(s):  
Hyperbolic Space ◽  
Limit Sets ◽  
Multiplicative Constant ◽  
Infinite Dimensional ◽  
Mass Redistribution ◽  
Isometric Actions

We generalize the mass redistribution principle and apply it to prove the Bishop–Jones relation for limit sets of metrically proper isometric actions on real infinite-dimensional hyperbolic space. We also show that the Hausdorff and packing measures on the limit sets of convex-cobounded groups are finite and positive and coincide with the conformal Patterson measure, up to a multiplicative constant.

scholarly journals The horofunction boundary of the infinite dimensional hyperbolic space

2019 ◽  
Vol 207 (1) ◽  
pp. 255-263
Author(s):  
Floris Claassens
Keyword(s):  
Hyperbolic Space ◽  
Infinite Dimensional ◽  
Real Hyperbolic Space

AbstractIn this paper we give a complete description of the horofunction boundary of the infinite dimensional real hyperbolic space, and characterise its Busemann points.

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