Let f be a smooth strictly convex solution ofdefined on R n , where a i , b i and c are constants, then the graph M ∇ f of ∇ f is a spacelike translating soliton for mean curvature flow in pseudo-Euclidean space R 2n n with the indefinite metric dx i dy i . In this paper, we classify the entire solutions of the PDE above for dimension n = 1 and show every entire classical strictly convex solution (n ≥ 2) must be a quadratic polynomial under a decay condition on the hessian (D 2 f ).

Li and Xu (Results Math 56:141-164, 2009) proved that any entire strictly convex C ∞ -solution of the Monge-Ampère equationwhere d0, d1,. . . ,dn are constants, must be a quadratic polynomial. Their result extends a well-known theorem of Jörgens-Calabi-Pogorelov. In our paper we will give a relatively simple proof for this extension in any dimension.Mathematics Subject Classfication. 53A15, 35J60, 53C40, 53C42.

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