We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.
SIAM J. Math. Anal., 29, no. 6, pp. 1419-1433. 1998
The surface diffusion flow for immersed hypersurfaces
Joachim Escher, Uwe Mayer, Gieri Simonett