7 citations · 24 across the 9 of their papers we have counts for
13 papers
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…
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…
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…
Repulsive Surfaces
Chris Yu, Caleb Brakensiek, Henrik Schumacher +1
Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific computing, but to date have ignored a very basic requirement: in many situa…
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…
Repulsive Curves
Christopher Yu, Henrik Schumacher, Keenan Crane
Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or sel…
Sobolev Gradients for the Möbius Energy
Philipp Reiter, Henrik Schumacher
Aiming at optimizing the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points of the Möbius energy.…
Computing the conformal barycenter
Jason Cantarella, Henrik Schumacher
The conformal barycenter of a point cloud on the sphere at infinity of the Poincaré ball model of hyperbolic space is a hyperbolic analogue of the geometric median of a point cloud…
Elastic energy regularization for inverse obstacle scattering problems
Julian Eckhardt, Ralf Hiptmair, Thorsten Hohage +2
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bend…
Variational Convergence of Discrete Elasticae
Sebastian Scholtes, Henrik Schumacher, Max Wardetzky
We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the…
Maximal discrete sparsity in parabolic optimal control with measures
Evelyn Herberg, Michael Hinze, Henrik Schumacher
We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method…
On -gradient Flows for the Willmore Energy
Henrik Schumacher
We show that the concept of -gradient flow for the Willmore energy and other functionals that depend at most quadratically on the second fundamental form is well-defined in th…
Variational Convergence of Discrete Minimal Surfaces
Henrik Schumacher, Max Wardetzky
Building on and extending tools from variational analysis, we prove Kuratowski convergence of sets of simplicial area minimizers to minimizers of the smooth Douglas-Plateau problem…