摘要
The author introduces the w-function defined on the considered spacelike graph M.Under the growth conditions w = o(log z) and w = o(r),two Bernstein type theorems for M in Rmn+ mare got,where z and r are the pseudo-Euclidean distance and the distance function on M to some fixed point respectively.As the ambient space is a curved pseudoRiemannian product of two Riemannian manifolds(Σ1,g1) and(Σ2,g2) of dimensions n and m,a Bernstein type result for n = 2 under some curvature conditions on Σ1 and Σ2 and the growth condition w = o(r) is also got.As more general cases,under some curvature conditions on the ambient space and the growth condition w = o(r) or w = o(√r),the author concludes that if M has parallel mean curvature,then M is maximal.
Abstract The author introduces the w-function defined on the considered spacelike graph M. Under the growth conditions w = o（log z） and w = o（r）, two Bernstein type theorems for M in Rm^n＋m are got, where z and r are the pseudo-Euclidean distance and the distance function on M to some fixed point respectively. As the ambient space is a curved pseudo- Riemannian product of two Riemannian manifolds （∑1,g1） and （∑2,g2） of dimensions n and m, a Bernstein type result for n =2 under some curvature conditions on E1 and E2 and the growth condition w = o（r） is also got. As more general cases, under some curvature conditions on the ambient space and the growth condition w = o（r） or w = o（√r）, the author concludes that if M has parallel mean curvature, then M is maximal.
