scholarly journals Examples of flag-wise positively curved spaces

2017 ◽  
Vol 52 ◽  
pp. 42-50 ◽  
Author(s):  
Ming Xu
Keyword(s):  
Curved Spaces ◽  
Positively Curved

scholarly journals Isometry groups of non-positively curved spaces: structure theory

2009 ◽  
Vol 2 (4) ◽  
pp. 661-700 ◽  
Author(s):  
Pierre-Emmanuel Caprace ◽  
Nicolas Monod
Keyword(s):  
Structure Theory ◽  
Isometry Groups ◽  
Curved Spaces ◽  
Positively Curved

scholarly journals A new proof of the Lie–Trotter–Kato formula in Hadamard spaces

2014 ◽  
Vol 16 (06) ◽  
pp. 1350044 ◽  
Author(s):  
Miroslav Bačák
Keyword(s):  
Weak Convergence ◽  
Short Note ◽  
Product Formula ◽  
Curved Spaces ◽  
Convex Functionals ◽  
Positively Curved

The Lie–Trotter–Kato product formula has been recently extended into Hadamard spaces by Stojkovic [Approximation for convex functionals on non-positively curved spaces and the Trotter–Kato product formula, Adv. Calc. Var. 5 (2012) 77–216]. The aim of our short note is to give a simpler proof relying upon weak convergence instead of an ultrapower technique.

scholarly journals An L1 ergodic theorem with values in a non-positively curved space via a canonical barycenter map

2012 ◽  
Vol 33 (2) ◽  
pp. 609-623 ◽  
Author(s):  
ANDRÉS NAVAS
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Ergodic Theorem ◽  
Point Theorem ◽  
General Version ◽  
Curved Space ◽  
Curved Spaces ◽  
The Core ◽  
Birkhoff Ergodic Theorem ◽  
Positively Curved

AbstractWe give a general version of the Birkhoff ergodic theorem for functions taking values in non-positively curved spaces. In this setting, the notion of a Birkhoff sum is replaced by that of a barycenter along the orbits. The construction of an appropriate barycenter map is the core of this note. As a byproduct of our construction, we prove a fixed point theorem for actions by isometries on a Buseman space.

scholarly journals Isometry groups of non-positively curved spaces: discrete subgroups

2009 ◽  
Vol 2 (4) ◽  
pp. 701-746 ◽  
Author(s):  
Pierre-Emmanuel Caprace ◽  
Nicolas Monod
Keyword(s):  
Isometry Groups ◽  
Discrete Subgroups ◽  
Curved Spaces ◽  
Positively Curved
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