Optimal mass transportation and Mather theory

  title={Optimal mass transportation and Mather theory},
  author={Patrick Bernard and B. Buffoni},
Several observations have recently renewed the interest for the classical topic of optimal mass transportation, whose primary origin is attributed to Monge a few years before French revolution. The framework is as follows. A space M is given, which in the present paper will be a compact manifold, as well as a continuous cost function c(x, y) : M ×M −→ R. Given two probability measures μ0 and μ1 on M , the mappings Ψ : M −→ M which transport μ0 into μ1 and minimize the total cost ∫ M c(x,Ψ(x))d… CONTINUE READING
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