In this doctoral thesis we investigate different area-minimizing geometric evolution equations for evolving hypersurfaces, which lie in a fixed domain and touch its boundary at a right angle. Additionally we consider situations where three evolving hypersurfaces meet each other at a triple line under prescribed angle conditions.
We introduce appropriate parametrizations to formulate the geometric evolution laws mean curvature and surface diffusion flow as partial differential equations for unknown functions. These differential equationsare then examined qualitatively on linearized stability around a stationary state.
More precisely, they are linearized around a stationary state and the arising linear differential equations are investigated on stability with the help of methods from spectral theory. As a result we get an equivalence of stability to positivity of a specific bilinear form, which is easier to verify in
applications
