Equilibrium of Surfaces in a Vertical Force Field

Abstract

In this paper, we study φ-minimal surfaces in R3 when the function φ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in R2. 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.