The affine Plateau problem

Details The affine Plateau problem The affine Plateau problem

2004-05-28

arxiv.org/abs/math/0405541v1

Mathematics

Differential Geometry

48 pages

Scientific paper

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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