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Stable approximations for axisymmetric Willmore flow for closed and open surfaces

Barrett, John W. ; Garcke, Harald ; Nürnberg, Robert



Abstract

For a hypersurface in Double-struck capital R-3, Willmore flow is defined as the L-2-gradient flow of the classical Willmore energy: the integral of the squared mean curvature. This geometric evolution law is of interest in differential geometry, image reconstruction and mathematical biology. In this paper, we propose novel numerical approximations for the Willmore flow of axisymmetric ...

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