Limit sets and convex cocompact groups in higher rank symmetric spaces

2018 ◽  
Vol 147 (1) ◽  
pp. 361-368
Author(s):  
Sungwoon Kim
Keyword(s):  
Symmetric Spaces ◽  
Limit Sets ◽  
Convex Cocompact ◽  
Higher Rank

scholarly journals A Characterization of Higher Rank Symmetric Spaces Via Bounded Cohomology

2009 ◽  
Vol 19 (1) ◽  
pp. 11-40 ◽  
Author(s):  
Mladen Bestvina ◽  
Koji Fujiwara
Keyword(s):  
Symmetric Spaces ◽  
Bounded Cohomology ◽  
Higher Rank

The spectrum and heat dynamics of locally symmetric spaces of higher rank

2014 ◽  
Vol 35 (5) ◽  
pp. 1524-1545 ◽  
Author(s):  
LIZHEN JI ◽  
ANDREAS WEBER
Keyword(s):  
Symmetric Spaces ◽  
Chaotic Behavior ◽  
Heat Semigroup ◽  
Locally Symmetric Spaces ◽  
Rank One ◽  
Higher Rank

The aim of this paper is to study the spectrum of the$L^{p}$Laplacian and the dynamics of the$L^{p}$heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank-one case, it turns out that the$L^{p}$heat semigroup on$M$has a certain chaotic behavior if$p\in (1,2)$, whereas for$p\geq 2$such chaotic behavior never occurs.

scholarly journals Symmetric spaces of higher rank do not admit differentiable compactifications

2009 ◽  
Vol 347 (4) ◽  
pp. 951-961 ◽  
Author(s):  
Benoît Kloeckner
Keyword(s):  
Symmetric Spaces ◽  
Higher Rank

scholarly journals Uniform convergence in the mapping class group

2008 ◽  
Vol 28 (4) ◽  
pp. 1177-1195 ◽  
Author(s):  
RICHARD P. KENT IV ◽  
CHRISTOPHER J. LEININGER
Keyword(s):  
Uniform Convergence ◽  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Limit Set ◽  
Limit Sets ◽  
Convex Cocompact ◽  
Zero Locus

AbstractWe characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact.

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