C02 Intrinsic convexity in the Mullins-Sekerka evolution

Intrinsic convexity was introduced and exploited by Otto and M. Westdickenberg to prove contraction estimates for the porous medium equation. The HED method to establish convergence of nonconvex gradient flows was developed by Otto and M. G. Westdickenberg and employed in joint work with Chugreeva for the Mullins-Sekerka (MS) evolution in two space dimensions. In this project we combine the insights of these previous works to hunt for “optimal convexity” of the MS problem in the plane.