Equilibrium of Surfaces in a Vertical Force Field

Source abstract

Abstract In this paper, we study $$\varphi$$ φ -minimal surfaces in $$\mathbb {R}^3$$ R 3 when the function $$\varphi$$ φ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in $$\mathbb {R}^2$$ R 2 . We describe a full classification of complete flat-embedded $$\varphi$$ φ -minimal surfaces if $$\varphi$$ φ is strictly monotone and characterize rotational $$\varphi$$ φ -minimal surfaces by its behavior at infinity when $$\varphi$$ φ has a quadratic growth.