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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Steiner problems in optimal transport


Author: Jonathan Dahl
Journal: Trans. Amer. Math. Soc. 363 (2011), 1805-1819
MSC (2010): Primary 49Q20; Secondary 90C35, 49J10
Published electronically: November 17, 2010
MathSciNet review: 2746666
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Abstract: We study the Steiner problem of finding a minimal spanning network in the setting of a space of probability measures with metric defined by the cost of optimal transport between measures. The existence of a solution is shown for the Wasserstein space $ P_p(\mathcal{X})$ over any base space $ \mathcal{X}$ which is a separable, locally compact Hadamard space. Structural results are given for the case $ P_2(\mathbb{R}^n)$.


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Additional Information

Jonathan Dahl
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Address at time of publication: Department of Mathematics, University of California, Berkeley, California 94720
Email: jdahl@math.jhu.edu, jdahl@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05065-2
PII: S 0002-9947(2010)05065-2
Received by editor(s): July 10, 2008
Published electronically: November 17, 2010
Additional Notes: The author would like to thank Chikako Mese for suggesting the problem and for many helpful discussions, as well as the referee for recommendations on an earlier draft.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.