The Monge Problem for Distance Cost in Geodesic Spaces

  title={The Monge Problem for Distance Cost in Geodesic Spaces},
  author={Stefano Bianchini},
We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dL is a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 19 references

A Course on Borel Sets

Graduate texts in mathematics • 2008
View 4 Excerpts
Highly Influenced

Geometric problems in the theory of dimensional distributions

V. N. Sudakov
Proc. Steklov Inst. Math., 141:1–178 • 1979
View 4 Excerpts
Highly Influenced

Ricci curvature bounds and geometric inequalities in the Heisenberg group

N. Juillet
View 2 Excerpts

The Euler-Lagrange equation for a singular variational problem

S. Bianchini, M. Gloyer
Math. Z. • 2009
View 1 Excerpt

The Monge problem in R

T. Champion, L. De Pascale

Optimal transport

C. Villani
old and new. Springer • 2008
View 1 Excerpt

A Course in Metric Geometry

Dmitri Burago, Yuri Burago, Sergei Ivanov

On the measure contraction property of metric measure spaces

S.-I. Ohta
Comment. Math. Helv., 82:805–828 • 2007
View 2 Excerpts

Similar Papers

Loading similar papers…