The parametric Willmore flow

Abstract

We establish a minimal positive existence time of the parametric Willmore flow for any smooth initial data (smooth immersion of a closed oriented surface). The minimal existence time is a function exclusively of geometric data which in particular are all well defined for general weak Lipschitz

immersions. This fact opens in particular the possibility for defining the Willmore flow for weak Lipschitz

W 2 , 2 W^{2,2}

initial data.