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Asymptotic plateau problem for prescribed mean curvature hypersurfaces

par Casteras, Jean-Baptiste ;Holopainen, Ilkka;Ripoll, Jaime Bruck
Référence Proceedings of the American Mathematical Society, 148, 4, page (1731-1743)
Publication Publié, 2020

Article révisé par les pairs

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Résumé :

We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds N. More precisely, given a suitable subset L of the asymptotic boundary of N and a suitable function H on N, we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature H provided that N satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.