Asymptotic Plateau problem for prescribed mean curvature hypersurfaces

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.

• Publication year

  2019

• Venue

  Proceedings of the American Mathematical Society

• Publication date

  2019-03-26

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1090/proc/14829arXiv 1903.11111
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

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• No concepts are published for this paper.

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