1. The Parametric Willmore Flow
- Author
-
Palmurella, Francesco and Rivière, Tristan
- Subjects
Mathematics - Differential Geometry ,Mathematics - Analysis of PDEs ,53E40, 53E10, 49Q10, 35K46, 53A05, 58E15, 58E30, 35J35, 35J48 - 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 $W^{2,2}$ immersions. This fact combined with the conservation law formulation of the equation given by the first author in 2008 opens the possibility for defining the Willmore flow for weak lipschitz $W^{2,2}$ initial data.
- Published
- 2023