3 citations · 4 across the 9 of their papers we have counts for
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Stability of the free boundary Willmore problem
Anna Dall'Acqua, Fabian Rupp, Reiner Schätzle +1
We study the Willmore problem with free boundary by means of a new Łojasiewicz-Simon gradient inequality for functionals on infinite dimensional manifolds. In contrast to previous…
The length-preserving elastic flow with free boundary on hypersurfaces in
Anna Dall'Acqua, Manuel Schlierf
We study the length-preserving elastic flow of curves in arbitrary codimension with free boundary on hypersurfaces. This constrained gradient flow is given by a nonlocal evolution…
Dimension reduction for Willmore flows of tori: fixed conformal class and analysis of singularities
Anna Dall'Acqua, Marius Müller, Fabian Rupp +1
This work studies Willmore flows of tori and their singularities via a dimension reduction approach. We introduce a Willmore flow that preserves the degenerate constraint of prescr…
Gradient flow dynamics for cell membranes in the Canham-Helfrich model
Fabian Rupp, Christian Scharrer, Manuel Schlierf
The energetically most efficient way how a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including…
Introducing spontaneous curvature to the Helfrich flow: Singularities and convergence
Manuel Schlierf
While there are various results on the long-time behavior of the Willmore flow, the Helfrich flow with non-zero spontaneous curvature as its natural generalization is not yet well-…
Global existence for the Willmore flow with boundary via Simon's Li-Yau inequality
Manuel Schlierf
It is well-known that the Willmore flow of closed spherical immersions exists globally in time and converges if the initial datum has Willmore energy below - exactly the Li-Ya…
Singularities of the hyperbolic elastic flow: Convergence, quantization and blow-ups
Manuel Schlierf
We study the elastic flow of closed curves and of open curves with clamped boundary conditions in the hyperbolic plane. While global existence and convergence toward critical point…
On the convergence of the Willmore flow with Dirichlet boundary conditions
Manuel Schlierf
Very little is yet known regarding the Willmore flow of surfaces with Dirichlet boundary conditions. We consider surfaces with a rotational symmetry as initial data and prove a glo…