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A Bernstein property of affine maximal hypersurfaces

Li, An-Min; Fang, Jia

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.