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Interior regularity of optimal transport paths

  • Qinglan Xia
Article

Abstract.

In a previous paper [12], we considered problems for which the cost of transporting one probability measure to another is given by a transport path rather than a transport map. In this model overlapping transport is frequently more economical. In the present article we study the interior regularity properties of such optimal transport paths. We prove that an optimal transport path of finite cost is rectifiable and simply a finite union of line segments near each interior point of the path.

Keywords

Probability Measure Line Segment Present Article Interior Point Regularity Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  • Qinglan Xia
    • 1
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

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