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<p>The problem of transporting graphs of continuous maps in a metric space with minimal cost is formulated. The <i>minimal cost distance</i> generated by this problem in the space of continuous maps is studied. The topology induced by this distance will be studied. A measure-theoretical version of the minimal cost distance will be given.</p>

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Optimal Transport of Maps

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Woochul Jung,
  • Carlos Morales,
  • Xiao Wen

摘要

The problem of transporting graphs of continuous maps in a metric space with minimal cost is formulated. The minimal cost distance generated by this problem in the space of continuous maps is studied. The topology induced by this distance will be studied. A measure-theoretical version of the minimal cost distance will be given.