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2. The Parametric Approach to the Willmore Flow

Author

Palmurella, Francesco and Rivière, Tristan

Subjects
Mathematics - Differential Geometry, Conformal gauge, General Mathematics, parabolic equations, 49Q10, 53A05, 58E15, 35J35, 35J48, 35K41, 35K91, Weak solutions, Willmore surfaces, Willmore gradient flow, Conformally invariant problems, Critical non linear 4th order elliptic, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, Analysis of PDEs (math.AP)
Abstract

We introduce a parametric framework for the study of Willmore gradient flows which enables to consider a general class of weak, energy-level solutions and opens the possibility to study energy quantization and finite-time singularities. We restrict in this first work to a small-energy regime and prove that, for small-energy weak immersions, the Cauchy problem in this class admits a unique solution., Advances in Mathematics, 400, ISSN:0001-8708, ISSN:1090-2082

Published
2020

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