Computing Minimal Surfaces via Level Set Curvature Flow

Given a fixed closed curve or curves in $R\sp3$, there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary. In this paper, a new approach to numerically solving the minimal surface problem is introduced. The surface is represented as a level set of a global function $\Phi:R\sp3\to R$. The family of surfaces evolve in time according to mean curvature flow. A solution is found when a steady state condition is achieved. A new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour. Several computer surfaces are shown including examples of topological changes.