Equilibrium of Surfaces in a Vertical Force Field

Abstract

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