Minimal Surfaces

Abstract

The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition to the basic terminology of differential geometry, we also focus on a classical theorem of minimal surfaces. It was referred as the Plateau’s Problem. This theorem states that a surface with the minimal area is a minimal surface and the proof of the theorem will be provided. To investigate when a ruled surface is minimal, we need to solve a system of differential equations. In conclusion, we find that only ruled surfaces that are also minimal are helicoids. Some graphs of minimal surfaces will also be provided in this project, using MAPLE and other computer programs.