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Existence of optimal transport maps for crystalline norms

Abstract:

We show the existence of optimal transport maps in the case when the cost function is the distance induced by a crystalline norm in ℝn, assuming that the initial distribution of mass is absolutely continuous with respect to ℒn. The proof is based on a careful decomposition of the space in transport rays induced by a secondary variational problem having the Euclidean distance as cost function. Moreover, improving a construction by Larman, we show the existence of a Nikodym set in ℝ3 having ful...

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Journal:
Duke Mathematical Journal
Volume:
125
Issue:
2
Pages:
201-241
Publication date:
2004-11-01
ISSN:
0012-7094
URN:
uuid:355c84e3-fccf-482d-b5c7-6da5c65c15fc
Source identifiers:
147668
Local pid:
pubs:147668
Language:
English

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