Stability of Spherical Caps under the Volume-Preserving Mean Curvature   Flow with Line Tension
  We show stability of spherical caps (SCs) lying on a flat surface, where the motion is governed by the volume-preserving Mean Curvature Flow (MCF). Moreover, we introduce a dynamic boundary condition that models a line tension effect on the boundary. The proof is based on the generalized principle of linearized stability 
Helmut Abels, Harald Garcke, Lars M\"uller
math.AP