Abstract
The surface diffusion equation is one of the geometric evolution laws and was first derived by Mullins [6] to model the development of surface grooves at the grain boundaries of a heated polycrystal. It is known that the surface diffusion equation is obtained as the H-1-gradient flow of the area functional for the evolving surfaces. Owing to this variational structure, we expect that the constant mean curvature surfaces (CMC surfaces) are steady states for this equation. In this paper, the criteria of the stability of the axisymmetric CMC surfaces will be studied with the help of the linearized stability analysis of the surface diffusion equation.
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