This result states bernstein theorem for entire minimal graphs and the bombieri–de giorgi–giusti threshold: given n N and let u: R n R be a function with u C 2(R n) satisfying the minimal surface equation div ( u 1 + | u| 2 ) = 0 on R n. If n 7, then u is affine. If n 8, there exist.... It is useful in the structure and regularity of minimal surfaces, where variational identities, curvature estimates, and compactness arguments control geometric objects.