Geometry of $[\varphi,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^{3}$

Abstract

In this survey we report a general and systematic approach to study $[\varphi,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^{3}$ from a geometric viewpoint and show some fundamental results obtained in the recent development of this theory.