Implications of Mean Curvature

There are several geometrical aspects of interface mean curvature that are particularly important when the interfacial energy is isotropic and the curvature becomes a driving force for mass transport. We present several equivalent cursory statements regarding mean curvature that have rigorous counterparts in differential geometry [6]. 

Level Set Surfaces Tangent Plane, Surface Normal, and Curvature 

The quantity 7/c may be regarded as the local potential due to the interface curvature to add a chemical species per unit volume of the species. On interfaces where the mean curvature is constant everywhere (such as on a sphere where k = 2/Rc, on a cylinder where k = 1/RC. and on a plane and a catenoid where k = 0), this potential is uniform and thus these are equilibrium interfaces. There is an infinite number of equilibrium interfaces a three-parameter family of minimal interfaces has been described [9]. 

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