scholarly journals Strong submultiplicativity of the Poincaré metric

2016 ◽  
Vol 24 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Daniela Kraus ◽  
Oliver Roth
Keyword(s):  
Poincaré Metric

scholarly journals Contractive curves

2002 ◽  
Vol 30 (4) ◽  
pp. 227-238 ◽  
Author(s):  
Araceli Bonifant ◽  
Marius Dabija
Keyword(s):  
Planar Domain ◽  
Plane Curves ◽  
Poincaré Metric

We discuss the dynamics of the correspondences associated to those plane curves whose local sections contract the Poincaré metric in a hyperbolic planar domain.

scholarly journals The Poincaré metric and isoperimetric inequalities for hyperbolic polygons

2005 ◽  
Vol 357 (10) ◽  
pp. 3905-3932 ◽  
Author(s):  
Roger W. Barnard ◽  
Petros Hadjicostas ◽  
Alexander Yu. Solynin
Keyword(s):  
Isoperimetric Inequalities ◽  
Poincaré Metric

scholarly journals On Lipschitz continuity with respect to the Poincaré metric of linear contractions between Möbius gyrovector spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Keiichi Watanabe
Keyword(s):  
Linear Operator ◽  
Lipschitz Continuity ◽  
Lipschitz Constant ◽  
Operator Norm ◽  
Inner Product ◽  
Product Spaces ◽  
Poincaré Metric ◽  
Lipschitz Continuous ◽  
Inner Product Spaces

AbstractFor every linear operator between inner product spaces whose operator norm is less than or equal to one, we show that the restriction to the Möbius gyrovector space is Lipschitz continuous with respect to the Poincaré metric. Moreover, the Lipschitz constant is precisely the operator norm.

scholarly journals On the logarithmic gradient of Poincaré metric

1994 ◽  
Vol 70 (7) ◽  
pp. 235-238
Author(s):  
Huang Xinzhong ◽  
Shigeyoshi Owa
Keyword(s):  
Poincaré Metric
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