Felix Knöppel
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View article: Going with the Flow
Going with the Flow Open
Given a sequence of poses of a body we study the motion resulting when the body is immersed in a (possibly) moving, incompressible medium. With the poses given, say, by an animator, the governing second-order ordinary differential equation…
View article: Random zero currents of sections of Hermitian line bundles over compact Riemannian manifolds
Random zero currents of sections of Hermitian line bundles over compact Riemannian manifolds Open
This paper is concerned with zero currents of random section of a Hermitian line bundle $E$ over a compact oriented Riemannian manifold. Given a metric connection, heat flow yields a natural 1-parameter family of probability measures on th…
View article: Rolling spheres and the Willmore energy
Rolling spheres and the Willmore energy Open
The Willmore energy plays a central role in the conformal geometry of surfaces in the conformal 3-sphere \(S^3\). It also arises as the leading term in variational problems ranging from black holes, to elasticity, and cell biology. In the …
View article: Constrained willmore surfaces
Constrained willmore surfaces Open
Smooth curves and surfaces can be characterized as minimizers of squared curvature bending energies subject to constraints. In the univariate case with an isometry (length) constraint this leads to classic non-linear splines. For surfaces,…
View article: Finding Conformal and Isometric Immersions of Surfaces
Finding Conformal and Isometric Immersions of Surfaces Open
We introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical experim…
View article: Commuting Hamiltonian flows of curves in real space forms
Commuting Hamiltonian flows of curves in real space forms Open
Starting from the vortex filament flow introduced in 1906 by Da Rios, there is a hierarchy of commuting geometric flows on space curves. The traditional approach relates those flows to the nonlinear Schrödinger hierarchy satisfied by the c…
View article: Complex line bundles over simplicial complexes
Complex line bundles over simplicial complexes Open
This cumulative dissertation treats practical and theoretical aspects of discrete vector bundles over simplicial complexes. Here the main focus is on discrete hermitian line bundles which, in recent years, found a number of remarkable appl…
View article: Complex Line Bundles Over Simplicial Complexes and Their Applications
Complex Line Bundles Over Simplicial Complexes and Their Applications Open
Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classific…