However, there are many others, for example the Mullins-Sekerka flow, the surface diffusion flow, or the Willmore flow. Follow this link if you want to see a few numerical simulations. Besides on free boundary problems I also work on nonpositively curved metric spaces, in particular on questions concerning gradients. Research Publications Clicking on a title will let you read an abstract and will give you download options. Electronic J. Diff.
Gradient flows on nonpositively curved metric spaces and harmonic maps .
SIAM J. Math. Contemporary Mathematics book series , Amer. Soc., Providence, Rhode Island, pp. A numerical scheme for free boundary problems that are gradient flows for the area functional . A singular example for the averaged mean curvature flow .