no. 1
The Plateau problem for convex curvature functions
[Le problème de Plateau pour des fonctions de courbure convexes]
Smith, Graham1
1 Instituto de Matemática, UFRJ, Av. Athos da Silveira Ramos 149, Centro de Tecnologia - Bloco C, Cidade Universitária - Ilha do Fundão, Caixa Postal 68530, 21941-909, Rio de Janeiro, RJ (Brazil)
Annales de l'Institut Fourier, Tome 70 (2020) no. 1, pp. 1-66.

Nous étudions le problème de Plateau paramétrique dans des variétés riemanniennes générales pour des hypersurfaces localement strictement convexes (LSC) et à courbure prescrite pour une classe générale de fonctions de courbure convexes. Nous établissons une condition scalaire pour l’existence de solutions dans le cas où il existe une barrière externe et la variété ambiante est une variété d’Hadamard

We present a novel and comprehensive approach to the study of the parametric Plateau problem for locally strictly convex (LSC) hypersurfaces of prescribed curvature for general convex curvature functions inside general Riemannian manifolds. We prove existence of solutions to the Plateau problem with outer barrier for LSC hypersurfaces of constant or prescribed curvature for general curvature functions inside general Hadamard manifolds modulo a single scalar condition. In particular, convex curvature functions of bounded type are fully treated.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3308
Classification : 58E12, 35J25, 35J60, 53C21, 53C42
Keywords: Plateau problem, non-linear elliptic PDEs
Mot clés : problème de Plateau, EDPs elliptiques non linéaires

Smith, Graham 1

1 Instituto de Matemática, UFRJ, Av. Athos da Silveira Ramos 149, Centro de Tecnologia - Bloco C, Cidade Universitária - Ilha do Fundão, Caixa Postal 68530, 21941-909, Rio de Janeiro, RJ (Brazil)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Smith, Graham. The Plateau problem for convex curvature functions. Annales de l'Institut Fourier, Tome 70 (2020) no. 1, pp. 1-66. doi : 10.5802/aif.3308. https://aif.centre-mersenne.org/articles/10.5802/aif.3308/

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