The affine Plateau problem

Trudinger, Neil; Wang, Xu-Jia

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

The affine Plateau problem

Authors: Neil S. Trudinger and Xu-Jia Wang
Journal: J. Amer. Math. Soc. 18 (2005), 253-289
MSC (2000): Primary 35J40; Secondary 53A15
DOI: https://doi.org/10.1090/S0894-0347-05-00475-3
Published electronically: January 3, 2005
MathSciNet review: 2137978
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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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