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arXiv · 1903.11111

Asymptotic Plateau problem for prescribed mean curvature hypersurfaces

Jean-Baptiste Casteras·Ilkka Holopainen·Jaime B. Ripoll
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Abstract

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.

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Jean-Baptiste Casteras, Ilkka Holopainen, Jaime B. Ripoll. 2019-11-20. Asymptotic Plateau problem for prescribed mean curvature hypersurfaces. https://doi.org/10.1090/proc%2F14829

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