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math.CA2025
On the Palais-Smale condition in geometric knot theory
Nicolas Freches, Henrik Schumacher, Daniel Steenebrügge +1
We prove that various families of energies relevant in geometric knot theory satisfy the Palais-Smale condition (PS) on submanifolds of arclength para\-metrized knots. These energi…
math.CA2021★ 6 cited
A speed preserving Hilbert gradient flow for generalized integral Menger curvature
Jan Knappmann, Henrik Schumacher, Daniel Steenebrügge +1
We establish long-time existence for a projected Sobolev gradient flow of generalized integral Menger curvature in the Hilbert case, and provide -bounds in time for the so…