On almost-fuchsian submanifolds of Hadamard spaces and the asymptotic Plateau problem
[Sur les sous-variétés presque-Fuchsiennes d’espaces de Hadamard et le problème de Plateau asymptotique]
Bronstein, Samuel1
1MPI-MIS, Inselstrasse 22, 04103 Leipzig (Germany)
Annales de l'Institut Fourier, Online first, 15 p.

We consider minimal submanifolds of negatively curved spaces with small curvature. We show that in a Hadamard space with negatively pinched curvature $-C\le K\le -1$, complete minimal submanifolds with second fundamental form less than $1$ everywhere bound a class of spheres at infinity for which the asymptotic Plateau problem is uniquely solvable.

Nous étudions les sous-variétés minimales de petite seconde forme fondamentale dans un espace de courbure de négative. Nous montrons que dans un espace de Hadamard de courbure négativement pincée entre $-C$ et $-1$, les sous-variétés minimales complètes de seconde forme fondamentales uniformément bornée par 1 bordent asymptotiquement une famille de sphères pour lesquelles le problème de Plateau asymptotique admet une unique solution.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3767
Classification : 53A10, 53C42
Keywords: Almost-fuchsian, minimal, Hadamard spaces, Plateau problem.
Mots-clés : Presque-fuchsien, minimal, espaces de Hadamard, problème de Plateau.

Bronstein, Samuel  1

1 MPI-MIS, Inselstrasse 22, 04103 Leipzig (Germany) 
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Bronstein, Samuel. On almost-fuchsian submanifolds of Hadamard spaces and the asymptotic Plateau problem. Annales de l'Institut Fourier, Online first, 15 p.

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