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## A Bernstein property of affine maximal hypersurfaces

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Author(s) : An-Min Li, Jia Fang

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 727-2002

MSC 2000

53A15 Affine differential geometry

Abstract :
Let $x:M^n\to A^{n+1}$ be the graph of some strictly convex function $x_{n+1} = f(x_1,\cdots,x_n)$ defined in a convex domain $|Omega\subset A^n$. We introduce a Riemannian metric $G^\# = \sum\frac{\partial^2 f}{\partial x_i \partial x_j}dx_idx_j$ on $M$. In this paper we investigate the affine maximal hypersurface which is complete with respect to the metric $G^\#$, and prove a Bernstein property for the affine maximal hypersurfaces.

Keywords : Bernstein property, affine maximal hypersurface