The surface diffusion flow for immersed hypersurfaces.

Joachim Escher, Uwe F. Mayer, Gieri Simonett

Abstract: 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.

1991 Subject Classification: 35R35, 35K55, 35S30, 65C20, 80A22

Key words and phrases: Surface diffusion, mean curvature, free boundary problem, immersed hypersurface, center manifold, maximal regularity, numerical simulation.

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