3 papers
math.CA2026
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.NA2025
Inverse obstacle scattering regularized by the tangent-point energy
Henrik Schumacher, Jannik Rönsch, Thorsten Hohage +1
We employ the so-called tangent-point energy as Tikhonov regularizer for ill-conditioned inverse scattering problems in 3D. The tangent-point energy is a self-avoiding functional o…
math.DG2025
On a Complete Riemannian Metric on the Space of Embedded Curves
Elias Döhrer, Philipp Reiter, Henrik Schumacher
We propose a new strong Riemannian metric on the manifold of (parametrized) embedded curves of regularity , . We highlight its close relationship to the (generali…