Author

Ruben Jakob

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Preprint Sep 2026

Hopf Reduction and Multiplicity-Resolved Endpoints for the Classical Willmore Flow of Hopf Tori

We establish an exact parametrized reduction of the classical Willmore flow of Hopf tori in the round three-sphere to the spherical elastic flow. In Willmore-flow time the reduction is $(\partial_t\gamma)^{\perp}=-4\nabla_{L^2}\mathcal E(\gamma)$; its global reconstruction uses a pullback-circle-bundle normalization an...

Mohameden Ahmedou, Ruben Jakob · 0 citations

Preprint Sep 2026

Uniqueness of Finite-Time Varifold Limits for the M\"obius-Invariant Willmore Flow

We prove uniqueness of finite-time geometric endpoints for the M\"obius-invariant Willmore flow in $\mathbb{S}^3$ under uniform quantitative nonumbilicity. The multiplicity-counting varifolds converge, without reparametrization or M\"obius renormalization, to a unique integral two-varifold. An intrinsic transport estim...

Mohameden Ahmedou, Ruben Jakob · 0 citations