Some existence results on the exterior Dirichlet problem for the minimal hypersurface equation
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 3, pp. 385-393.
corrigé par Erratum

It is proved the existence of solutions to the exterior Dirichlet problem for the minimal hypersurface equation in complete noncompact Riemannian manifolds either with negative sectional curvature and simply connected or with nonnegative Ricci curvature under a growth condition on the sectional curvature.

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     author = {do Esp{\'\i}rito-Santo, Nedir and Ripoll, Jaime},
     title = {Some existence results on the exterior {Dirichlet} problem for the minimal hypersurface equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {385--393},
     publisher = {Elsevier},
     volume = {28},
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     doi = {10.1016/j.anihpc.2011.02.007},
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     zbl = {1219.58006},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.007/}
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do Espírito-Santo, Nedir; Ripoll, Jaime. Some existence results on the exterior Dirichlet problem for the minimal hypersurface equation. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 3, pp. 385-393. doi : 10.1016/j.anihpc.2011.02.007. http://www.numdam.org/articles/10.1016/j.anihpc.2011.02.007/

[1] J. Cheeger, D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96 (1972), 413-443 | MR | Zbl

[2] H.I. Choi, Asymptotic Dirichlet problem for harmonic functions on Riemannian manifolds, Trans. Amer. Math. Soc. 281 (1984), 691-716 | MR | Zbl

[3] M. Dajczer, J.H. De Lira, Killing graphs with prescribed mean curvature and Riemannian submersions, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 763-775 | EuDML | Numdam | MR | Zbl

[4] N. Do Espírito-Santo, S. Fornari, J. Ripoll, The Dirichlet problem for the minimal hypersurface equation in M× with prescribed asymptotic boundary, J. Math. Pures Appl. 93 no. 2 (2010), 204-221 | MR | Zbl

[5] S. Fornari, J. Ripoll, Killing fields, mean curvature, translation maps, Illinois J. Math. 48 no. 4 (2004), 1385-1402 | MR | Zbl

[6] J.A. Gálvez, H. Rosenberg, Minimal surfaces and harmonic diffeomorphisms from the complex plane onto certain Hadamard surfaces, Amer. J. Math. 132 (2010), 1249-1273 | MR | Zbl

[7] N. Kutev, F. Tomi, Existence and nonexistence results for the exterior Dirichlet problem for the minimal surface equation in the plane, Differential Integral Equations 6 (1998), 917-928 | MR | Zbl

[8] L. Mazet, M.M. Rodríguez, H. Rosenberg, The Dirichlet problem for the minimal surface equation with possible infinite boundary data over domains in a Riemannian surface, preprint. | MR

[9] J.C.C. Nitsche, Vorlesungen über Minimal Flächen, Springer-Verlag, Berlin, Heidelberg, New York (1975) | MR | Zbl

[10] H. Rosenberg, Minimal surfaces in M×, Illinois J. Math. 46 (2002), 1177-1195 | MR | Zbl

[11] J. Ripoll, M. Telichevesky, Asymptotic Dirichlet problems for Laplaceʼs and minimal equations on Hadamard manifolds, preprint.

[12] R. Schoen, S.T. Yau, Lectures on Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, vol. I, International Press. | MR

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