The Plateau problem from the perspective of optimal transport

Haïm Brezis (1, 2, 3) , Petru Mironescu (4, 5)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Department of Mathematics - Rutgers School of Arts and Sciences
3 TECHNION - Department of Mathematics
4 EDPA - Équations aux dérivées partielles, analyse
5 ICJ - Institut Camille Jordan

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.

Mots clés: Krein-Milman; extreme points; Monge-Kantorovich; Plateau problem; Optimal transport

Domaines: Analyse classique [math.CA]

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⟩