The parametric Willmore flow

Author:

Palmurella Francesco1,Rivière Tristan2

Affiliation:

1. Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa , Italy

2. Department of Mathematics , ETH Zentrum , CH-8093 Zürich , Switzerland

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.

Publisher

Walter de Gruyter GmbH

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