16 citations · 53 across the 9 of their papers we have counts for
9 papers
Conservation, convergence, and computation for evolving heterogeneous elastic wires
Anna Dall'Acqua, Gaspard Jankowiak, Leonie Langer +1
The elastic energy of a bending-resistant interface depends both on its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a…
Curvature-dependent Eulerian interfaces in elastic solids
Katharina Brazda, Martin Kružík, Fabian Rupp +1
We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a f…
Short closed geodesics and the Willmore energy
Marius Müller, Fabian Rupp, Christian Scharrer
We prove a lower bound on the length of closed geodesics for spheres with Willmore energy below . The energy threshold is optimal and the inequality cannot be extended to surfa…
Optimal thresholds for preserving embeddedness of elastic flows
Tatsuya Miura, Marius Müller, Fabian Rupp
We consider elastic flows of closed curves in Euclidean space. We obtain optimal energy thresholds below which elastic flows preserve embeddedness of initial curves for all time. T…
The Willmore flow with prescribed isoperimetric ratio
Fabian Rupp
We introduce a non-local -gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an e…
A Li-Yau inequality for the 1-dimensional Willmore energy
Marius Müller, Fabian Rupp
By the classical Li-Yau inequality, an immersion of a closed surface in with Willmore energy below has to be embedded. We discuss analogous results for curves i…
The volume-preserving Willmore flow
Fabian Rupp
We consider a closed surface in evolving by the volume-preserving Willmore flow and prove a lower bound for the existence time of smooth solutions. For spherical ini…
Existence and convergence of the length-preserving elastic flow of clamped curves
Fabian Rupp, Adrian Spener
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative -gradient flow of the elastic energy. For any initial curve lying mer…
On the Lojasiewicz-Simon gradient inequality on submanifolds
Fabian Rupp
We provide sufficient conditions for the Lojasiewicz-Simon gradient inequality to hold on a submanifold of a Banach space and discuss the optimality of our assumptions. Our result…