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