Some questions on integral geometry on noncompact symmetric spaces of higher rank

2012 ◽  
Vol 170 (2) ◽  
pp. 195-203 ◽  
Author(s):  
E. K. Narayanan ◽  
A. Sitaram
Keyword(s):  
Integral Geometry ◽  
Symmetric Spaces ◽  
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

scholarly journals Integral geometry under cut loci in compact symmetric spaces

1995 ◽  
Vol 137 ◽  
pp. 33-53 ◽  
Author(s):  
Hiroyuki Tasaki
Keyword(s):  
Invariant Measure ◽  
Lie Group ◽  
Integral Geometry ◽  
Symmetric Spaces ◽  
Homogeneous Spaces ◽  
Integral Invariant ◽  
Identity Component ◽  
Integral Invariants ◽  
Compact Symmetric Spaces ◽  
Group Of Isometries

The theory of integral geometry has mainly treated identities between integral invariants of submanifolds in Riemannian homogeneous spaces like as dμg(g) where M and N are submanifolds in a Riemannian homogeneous spaces of a Lie group G and I(M ∩ gN) is an integral invariant of M ∩ gN. For example Poincaré’s formula is one of typical identities in integral geometry, which is as follows. We denote by M(R2) the identity component of the group of isometries of the plane R2 with a suitable invariant measure μM(R2).

Offbeat Integral Geometry on Symmetric Spaces

2013 ◽  
Author(s):  
Valery V. Volchkov ◽  
Vitaly V. Volchkov
Keyword(s):  
Integral Geometry ◽  
Symmetric Spaces

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.

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