Abstract
In this paper we consider the Willmore flow in three space dimensions. We prove that embedded surfaces can be driven to a self-intersection in finite time. This situation is in strict contrast to the behavior of hypersurfaces under the mean curvature flow, where the maximum principle prevents self-intersections, but very much analogous to the surface diffusion flow.
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Mayer, U.F., Simonett, G. (2003). Self-Intersections for Willmore Flow. In: Iannelli, M., Lumer, G. (eds) Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics. Progress in Nonlinear Differential Equations and Their Applications, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8085-5_24
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DOI: https://doi.org/10.1007/978-3-0348-8085-5_24
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9433-3
Online ISBN: 978-3-0348-8085-5
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