The Willmore flow with prescribed isoperimetric ratio

Abstract

We introduce a non-local $L^2$-gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, we show long-time existence and convergence to a Helfrich immersion. This is in sharp contrast to the locally constrained flow, where finite time singularities occur.

Final version. 30 pages, 1 figure. To appear in Comm. Partial Differential Equations

References in corpus (5)

• Surface diffusion flow near spheres
• Lifespan theorem for constrained surface diffusion flows
• The volume-preserving Willmore flow
• A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint
• Embedded Delaunay tori and their Willmore energy

Cited by in corpus (2)

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