Equilibrium of Surfaces in a Vertical Force Field

2019/10/17 by Martínez, Antonio, Martínez-Triviño, A. L. · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.07795

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.

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