The Caratheodory Distance Does not Define the Toplogy

1984 ◽  
Vol 91 (2) ◽  
pp. 223 ◽  
Author(s):  
Jean-Pierre Vigue
Keyword(s):  
Carathéodory Distance

MASS TRANSPORTATION IN GROUPS OF TYPE H

2005 ◽  
Vol 07 (04) ◽  
pp. 509-537 ◽  
Author(s):  
S. RIGOT
Keyword(s):  
Cost Function ◽  
Optimal Transport ◽  
Transport Problem ◽  
Mass Transportation ◽  
Heisenberg Groups ◽  
The One ◽  
Carathéodory Distance ◽  
The Cost ◽  
Special Case

We give a solution of the optimal transport problem in groups of type H when the cost function is the square of either the Carnot–Carathéodory or Korányi distance. This generalizes results previously proved for the Heisenberg groups. We use the same strategy that the one which was developed in that special case together with slightly refined technicalities that essentially reflect the fact that the center of the group can be of dimension larger than one. For each distance we prove existence, uniqueness and give a characterization of the optimal transport. In the case of the Carnot–Carathéodory distance we also prove that the optimal transport arises as the limit of the optimal transports in natural Riemannian approximations.

scholarly journals The inner Carathéodory distance for the annulus. II.

1993 ◽  
Vol 40 (2) ◽  
pp. 393-398
Author(s):  
Marek Jarnicki ◽  
Peter Pflug
Keyword(s):  
Carathéodory Distance
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