A Bernstein type theorem for minimal volume preserving maps (Q2781272)

A map between two Riemannian manifolds \(M_1,M_2\) is called minimal if its graph is a minimal submanifold of \(M_1\times M_2\). Bernstein's theorem [\textit{S. Bernstein}, Char'kov, Comm. Soc. Math. 15, 38-45 (1917; JFM 48.1401.01)] (stating that any minimal map from \(\mathbb{R}^2\) to \(\mathbb{R}\) must be linear), was generalized by several authors. One of them is the present author, who derives here that any minimal volume preserving map from \(\mathbb{R}^2\) into \(\mathbb{R}^2\) is a linear diffeomorphism, by using that any minimal diffeomorphism of \(\mathbb{R}^2\) is linear.