On the Jacobian of minimal graphs in R^4

We provide a characterization for complex analytic curves among two-dimensional minimal graphs in $\mathbb{R}^{4}$ via the Jacobia

Complete minimal hypersurfaces in the hyperbolic space H4\mathbb{H}^4 with vanishing Gauss-Kronecker curvature

We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below