Isoperimetric Hardy Type and Poincaré Inequalities on Metric Spaces

2009 ◽  
pp. 285-298
Author(s):  
Joaquim Martín ◽  
Mario Milman
Keyword(s):  
Metric Spaces ◽  
Poincaré Inequalities ◽  
Hardy Type ◽  
Poincare Inequalities

scholarly journals Poincaré inequalities, embeddings, and wild groups

2011 ◽  
Vol 147 (5) ◽  
pp. 1546-1572 ◽  
Author(s):  
Assaf Naor ◽  
Lior Silberman
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Isometric Action ◽  
Metric Embedding ◽  
Random Group ◽  
Cartesian Products ◽  
Poincaré Inequalities ◽  
Embedding Theory ◽  
Geometric Conditions ◽  
Poincare Inequalities

AbstractWe present geometric conditions on a metric space (Y,dY) ensuring that, almost surely, any isometric action onYby Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov–Hausdorff limits, and Cartesian products. We use methods from metric embedding theory to establish the validity of these conditions for a variety of classes of metric spaces, thus establishing new fixed point results for actions of Gromov’s ‘wild groups’.

Poincaré inequalities for linearizations of very fast diffusion equations

Nonlinearity ◽  
2002 ◽  
Vol 15 (3) ◽  
pp. 565-580 ◽  
Author(s):  
J A Carrillo ◽  
C Lederman ◽  
P A Markowich ◽  
G Toscani
Keyword(s):  
Diffusion Equations ◽  
Fast Diffusion ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Fast Diffusion Equations
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