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The affine Plateau problem |
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| Authors: | Neil S Trudinger Xu-Jia Wang |
| Institution: | Centre for Mathematics and Its Applications, The Australian National University, Canberra, ACT 0200, Australia ; Centre for Mathematics and Its Applications, Australian National University, Canberra, ACT 0200, Australia |
| 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. |
| Keywords: | Affine Plateau problem affine maximal hypersurface affine area functional affine maximal surface equation variational problem second boundary value problem a priori estimates strict convexity interior regularity Bernstein Theorem Monge-Amp\`{e}re measure curvature measure Gauss mapping locally convex hypersurface generalized Legendre transform |
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