On the asymptotic Plateau problem for area minimizing surfaces in $${\mathbb {E}}(-1,\tau )$$

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.2000 Mathematics Subject Classification. 53A10, 53C42, 49Q05, 49Q20.

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On the asymptotic Plateau problem for area minimizing surfaces in $${\mathbb {E}}(-1,\tau )$$

Cited by 2 publications

References 9 publications

On the asymptotic Plateau problem in SL˜2(R)

On the asymptotic Plateau problem in SL˜2(R)

Asymptotic Plateau problem for prescribed mean curvature hypersurfaces

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