The Willmore flow with prescribed isoperimetric ratio (2106.02579v3)

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.