Willmore flow

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The Willmore flow in differential geometry corresponds to the L2-gradient flow of the Willmore energy.

e[{\mathcal{M}}]=\frac{1}{2} \int_{\mathcal{M}} H^2\, \mathrm{d}A

where H stands for the mean curvature of the manifold \mathcal{M}. It is named after the English differential geometer Tom Willmore.

This flow leads to an evolution problem in differential geometry: the surface \mathcal{M} is evolving in time to follow variations of steepest descent of the energy. Like surface diffusion it is a fourth-order flow, since the variation of the energy contains fourth derivatives.

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