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Journal Articles Comptes Rendus. Mathématique Year : 2019

The Plateau problem from the perspective of optimal transport

Abstract

Both optimal transport and minimal surfaces have received much attention in recent years. We show that the methodology introduced by Kantorovich on the Monge problem can, surprisingly, be adapted to questions involving least area, e.g. Plateau type problems as investigated by Federer.
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Dates and versions

hal-02197057 , version 1 (30-07-2019)
hal-02197057 , version 2 (05-08-2019)
hal-02197057 , version 3 (01-09-2019)

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Haïm Brezis, Petru Mironescu. The Plateau problem from the perspective of optimal transport. Comptes Rendus. Mathématique, 2019, 357 (7), pp.597-612. ⟨10.1016/j.crma.2019.07.007⟩. ⟨hal-02197057v3⟩
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