The Perron Method and the Non-Linear Plateau Problem

Andrew Clarke; Graham Smith

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arXiv · 0912.2892

The Perron Method and the Non-Linear Plateau Problem

Andrew Clarke·Graham Smith

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Abstract

We describe a novel technique for solving the Plateau problem for constant curvature hypersurfaces based on recent work of Harvey and Lawson. This is illustrated by an existence theorem for hypersurfaces of constant Gaussian curvature in $\Bbb{R}^{n+1}$.

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Andrew Clarke, Graham Smith. 2009-12-15. The Perron Method and the Non-Linear Plateau Problem. https://arxiv.org/abs/0912.2892

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