The Apollonian Metric: The Comparison Property, Bilipschitz Mappings and Thick Sets

2006 ◽  
Vol 12 (2) ◽  
Author(s):  
P. A. Hästö
Keyword(s):  
Apollonian Metric ◽  
Bilipschitz Mappings ◽  
Comparison Property

scholarly journals The Apollonian metric: limits of the comparison and bilipschitz properties

2003 ◽  
Vol 2003 (20) ◽  
pp. 1141-1158 ◽  
Author(s):  
Peter A. Hästö
Keyword(s):  
Large Class ◽  
Half Space ◽  
Hyperbolic Metric ◽  
Comparison Results ◽  
The Hyperbolic Metric ◽  
Apollonian Metric ◽  
Bilipschitz Mappings

The Apollonian metric is a generalization of the hyperbolic metric. It is defined in arbitrary domains inℝn. In this paper, we derive optimal comparison results between this metric and thejGmetric in a large class of domains. These results allow us to prove that Euclidean bilipschitz mappings have small Apollonian bilipschitz constants in a domainGif and only ifGis a ball or half-space.

Conformality of the Apollonian Metric

2004 ◽  
Vol 3 (2) ◽  
pp. 397-411 ◽  
Author(s):  
Zair Ibragimov
Keyword(s):  
Apollonian Metric

Isometries of the Half-Apollonian Metric

2004 ◽  
Vol 49 (6) ◽  
pp. 405-415 ◽  
Author(s):  
Peter Hästö * ◽  
Henri Lindén
Keyword(s):  
Apollonian Metric

John disks, the Apollonian metric, and min-max properties

2010 ◽  
Vol 120 (1) ◽  
pp. 83-96
Author(s):  
M. Huang ◽  
S. Ponnusamy ◽  
X. Wang
Keyword(s):  
Apollonian Metric

scholarly journals Non-Existence Results for Stable Solutions to Weighted Elliptic Systems Including Advection Terms

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 252
Author(s):  
Suleman Alfalqi
Keyword(s):  
Elliptic Systems ◽  
Existence Results ◽  
Liouville Type ◽  
Non Linear ◽  
Liouville Type Theorems ◽  
Stable Solutions ◽  
Bootstrap Iteration ◽  
Comparison Property

In this paper, we study a non-linear weighted Grushin system including advection terms. We prove some Liouville-type theorems for stable solutions of the system, based on the comparison property and the bootstrap iteration. Our results generalise and improve upon some previous works.

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