Non-archimedean transportation problems and Kantorovich ultra-norms

M. Megrelishvili, M. Shlossberg

Research output: Contribution to journalArticlepeer-review


We study a non-archimedean (NA) version of transportation problems and introduce naturally arising ultra-norms which we call Kantorovich ultra-norms. For every ultra-metric space and every NA valued field (e.g., the field Qp of p-adic numbers) the naturally defined inf-max cost formula achieves its infimum. We also present NA versions of the Arens-Eells construction and of the integer value property. We introduce and study free NA locally convex spaces. In particular, we provide conditions under which these spaces are normable by Kantorovich ultra-norms and also conditions which yield NA versions of Tkachenko-Uspenskij theorem about free abelian topological groups.

Original languageEnglish
Pages (from-to)125-148
Number of pages24
JournalP-Adic Numbers, Ultrametric Analysis, and Applications
Issue number2
StatePublished - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2016, Pleiades Publishing, Ltd.


  • Fermat-Torricelli point
  • Kantorovich ultra-norm
  • Kantorovich-Rubinstein seminorm
  • Levi-Civita field
  • free abelian topological group
  • free locally convex space
  • non-archimedean valuation
  • p-adic numbers
  • transportation problem
  • valued field


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