In this dissertation we study minimal surfaces. That is, two-dimensional objects whose area is locally minimal. Using the calculus of variations we will derive the Euler-Lagrange differential equation which has to be fulfilled for explicitly given minimal surfaces. Further, we will show that a parametric surface is minimal if and only if its mean curvature equals zero. Finally, we will present an example which points out that a minimal surface is not always a global extreme. This means that, given boundary conditions, there may exist several minimal surfaces with different areas.
|
