Equilibrium of Surfaces in a Vertical Force Field

Abstract

In this paper we study $\phi$-minimal surfaces in ${\mathbb{R}}^3$ when the function $\phi$ 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 $\phi$-minimal surfaces if $\phi$ is strictly monotone and characterize rotational $\phi$-minimal surfaces by its behavior at infinity when $\phi$ has a quadratic growth.

30 pages, 9 figures