97 citations · 390 across the 25 of their papers we have counts for
20 papers · 1 filter
Conformal Surface Splines
Yousuf Soliman, Ulrich Pinkall, Peter Schröder
We introduce a family of boundary conditions and point constraints for conformal immersions that increase the controllability of surfaces defined as minimizers of conformal variati…
Elastic Curves with Variable Bending Stiffness
Oliver Gross, Ulrich Pinkall, Moritz Wahl
We study stationary points of the bending energy of curves subject to constraints on the arc-length and the curve's holonomy while simultaneously allo…
Rolling spheres and the Willmore energy
Felix Knöppel, Ulrich Pinkall, Peter Schröder +1
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…
A discrete version of Liouville's theorem on conformal maps
Ulrich Pinkall, Boris Springborn
Liouville's theorem says that in dimension greater than two, all conformal maps are Möbius transformations. We prove an analogous statement about simplicial complexes, where two si…
Finding Conformal and Isometric Immersions of Surfaces
Albert Chern, Felix Knöppel, Franz Pedit +2
We introduce a family of variational functionals for spinor fields on a compact Riemann surface that can be used to find close-to-conformal immersions of into $\mathbb{R}^3…
Commuting Hamiltonian flows of curves in real space forms
Albert Chern, Felix Knöppel, Franz Pedit +1
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 flow…
A Weierstrass representation for 2D elasticity
Ulrich Pinkall, Jonas Tervooren
We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a f…
Complex Line Bundles over Simplicial Complexes and their Applications
Felix Knöppel, Ulrich Pinkall
Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Dis…
Isothermic triangulated surfaces
Wai Yeung Lam, Ulrich Pinkall
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admit…
Conformal deformations of immersed discs in and elliptic boundary value problems
Christoph Bohle, Ulrich Pinkall
Boundary value problems for operators of Dirac type arise naturally in connection with the conformal geometry of surfaces immersed in Euclidean 3--space. Recently such boundary val…
Elastic strips
David Chubelaschwili, Ulrich Pinkall
Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we w…
Isothermic submanifolds of symmetric -spaces
F. E. Burstall, N. M. Donaldson, F. Pedit +1
We extend the classical theory of isothermic surfaces in conformal 3-space, due to Bour, Christoffel, Darboux, Bianchi and others, to the more general context of submanifolds of sy…
The spectral curve of a quaternionic holomorphic line bundle over a 2-torus
Christoph Bohle, Franz Pedit, Ulrich Pinkall
A conformal immersion of a 2-torus into the 4-sphere is characterized by an auxiliary Riemann surface, its spectral curve. This complex curve encodes the monodromies of a certain D…
Discrete holomorphic geometry I. Darboux transformations and spectral curves
Christoph Bohle, Franz Pedit, Ulrich Pinkall
Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete dif…
Conformal maps from a 2-torus to the 4-sphere
C. Bohle, K. Leschke, F. Pedit +1
We study the space of conformal immersions of a 2-torus into the 4-sphere. The moduli space of generalized Darboux transforms of such an immersed torus has the structure of a Riema…
Constrained Willmore Surfaces
Christoph Bohle, G. Paul Peters, Ulrich Pinkall
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy under compactly supported infinitesimal conf…
Willmore tori in the 4-sphere with nontrivial normal bundle
K. Leschke, F. Pedit, U. Pinkall
We characterize Willmore tori in the 4-sphere with nontrivial normal bundle as Twistor projections of elliptic curves in complex projective space or as inverted minimal tori (with…
Schwarzian Derivatives and Flows of Surfaces
Francis Burstall, Franz Pedit, Ulrich Pinkall
This paper goes some way in explaining how to construct an integrable hierarchy of flows on the space of conformally immersed tori in n-space. These flows have first occured in mat…
Quaternionic holomorphic geometry: Pluecker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori
D. Ferus, K. Leschke, F. Pedit +1
The paper develops the fundamentals of quaternionic holomorphic curve theory. The holomorphic functions in this theory are conformal maps from a Riemann surface into the 4-sphere,…
Conformal Geometry of Surfaces in the 4-Sphere and Quaternions
F. Burstall, D. Ferus, K. Leschke +2
This is the first comprehensive introduction to the authors' recent attempts toward a better understanding of the global concepts behind spinor representations of surfaces in 3-spa…