The Parametric Willmore Flow

2023/08/06 by Francesco Palmurella, Palmurella, Francesco, Tristan Rivière +1 · 1 citation
Engineering · Mathematics · #35J35 #35J48 #35K46 #49Q10 #53A05 #53E10 #53E40 #58E15 #58E30 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2308.03144

openalex publication_date 2023/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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