Francesco Palmurella - The parametric approach to the Willmore flow

We introduce a parametric framework for the study of Willmore gradient flows which enables to consider a general class of weak, energy-level solutions and opens the possibility to study energy quantization and finite-time singularities.

In this first work we restricted to a small-energy regime and proved that, for small-energy weak immersions, the Cauchy problem in this class admits a unique solution.