The affine Plateau problem

Trudinger, Neil; Wang, Xu-Jia

doi:10.1090/S0894-0347-05-00475-3

The affine Plateau problem
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by Neil S. Trudinger and Xu-Jia Wang

J. Amer. Math. Soc. 18 (2005), 253-289

DOI: https://doi.org/10.1090/S0894-0347-05-00475-3

Published electronically: January 3, 2005

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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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