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The affine Plateau problem

Neil S. Trudinger·Xu-Jia Wang
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Abstract

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.

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Neil S. Trudinger, Xu-Jia Wang. 2004-05-28. The affine Plateau problem. https://arxiv.org/abs/math/0405541

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