The Plateau problem for convex curvature functions
Annales de l'Institut Fourier, Volume 70 (2020) no. 1, pp. 1-66.

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.

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

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DOI: 10.5802/aif.3308
Classification: 58E12,  35J25,  35J60,  53C21,  53C42
Keywords: Plateau problem, non-linear elliptic PDEs
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)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Smith, Graham. The Plateau problem for convex curvature functions. Annales de l'Institut Fourier, Volume 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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