Willmore flow

Summary

The Willmore flow is the gradient flow of the Willmore energy for closed surfaces immersed in $\R^3$. Each point of the surface moves along the normal with a speed given by a fourth-order expression in the surface. In this way the energy decreases as fast as possible. Its stationary surfaces are the Willmore surfaces, such as round spheres. It is a tool for finding surfaces that minimize bending energy.