Parametric Approaches for Geometric Evolution Equations and Interfaces

In this chapter we will give an overview of different parametric methods for dealing with interfaces. Related to the evolution of interfaces are geometric evolution equations for curves and surfaces. We will present analytical and numerical tools mainly for geometric evolution equations. However, typically they can also be used for more complex models also involving bulk quantities. For parametric models for more complex interface problems we only sketch ideas and do not go into analytical details and refer to the literature for a more precise account of results and proofs.