On the entire self-shrinking solutions to Lagrangian mean curvature flow II

We prove the rigidity of entire graphic Lagrangian self-shrinkers in $$({\mathbb {R}}^{2n}, g_\tau )$$ , where $$g_\tau =\sin \tau \,\delta _0+\cos \,g_0$$ is a linear combination Euclidean metric $$\delta _0$$ and pseudo $$g_0=2\sum _i dx_idy_i$$ with $$\tau \in (0,\frac{\pi }{2})$$ complementing previous results for =0$$ =\frac{\pi }{2}$$ ; actually we obtain Bernstein theorems three corresponding nonlinear elliptic equations between Monge–Ampère equation ( ) special ). Moreover, find theorem fails when (-\frac{\pi }{4},0)$$ spacelike self-shrinker Minkowski spaces share this non-rigidity property.