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 in [5] 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.
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