Willmore Flow of Complete Surfaces

Abstract

We consider the Willmore flow equation for complete, properly immersed surfaces in Rn. Given bounded geometry on the initial surface, we extend the result by Kuwert and Schätzle in 2002 and prove short time existence and uniqueness of the Willmore flow. We also show that a complete Willmore surface with low Willmore energy must be a plane, and that a Willmore flow with low initial energy and Euclidean volume growth must converge smoothly to a plane.

arXiv comment47 pages

References in corpus (7)

• Surface diffusion flow near spheres
• A classification theorem for Helfrich surfaces
• Lifespan theorem for constrained surface diffusion flows
• Lifespan theorem for simple constrained surface diffusion flows
• The volume-preserving Willmore flow
• The Parametric Approach to the Willmore Flow
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Cited by in corpus (1)

• The free elastic flow for closed planar curves