The parametric Willmore flow

Abstract

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 W 2 , 2 W^{2,2} immersions. This fact opens in particular the possibility for defining the Willmore flow for weak Lipschitz W 2 , 2 W^{2,2} initial data.