19 citations · 31 across the 8 of their papers we have counts for
8 papers
Bonnet pairs, isothermic surfaces and the retraction form
F. E. Burstall, T. Hoffmann, F. Pedit +1
We give a modern account of the classical theory of Bianchi \cite{Bia03} (see also \cite{KamPedPin98}) relating isothermic surfaces to Bonnet pairs. The main novelty is to identify…
Skew parallelogram nets and universal factorization
Tim Hoffmann, Andrew O. Sageman-Furnas, Jannik Steinmeier
We obtain many objects of discrete differential geometry as reductions of skew parallelogram nets, a system of lattice equations that may be formulated for any unit associative alg…
Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elastica
Alexander I. Bobenko, Tim Hoffmann, Andrew O. Sageman-Furnas
In 1883, Darboux gave a local classification of isothermic surfaces with one family of planar curvature lines using complex analytic methods. His choice of real reduction cannot co…
Compact Bonnet Pairs: isometric tori with the same curvatures
Alexander I. Bobenko, Tim Hoffmann, Andrew O. Sageman-Furnas
We explicitly construct a pair of immersed tori in three dimensional Euclidean space that are related by a mean curvature preserving isometry. These Bonnet pair tori are the first…
Topology determines force distributions in one-dimensional random spring networks
Knut M. Heidemann, Andrew O. Sageman-Furnas, Abhinav Sharma +3
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technolog…
Topology counts: force distributions in circular spring networks
Knut M. Heidemann, Andrew O. Sageman-Furnas, Abhinav Sharma +3
Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous and, althou…
A 2x2 Lax representation, associated family, and Bäcklund transformation for circular K-nets
Tim Hoffmann, Andrew O. Sageman-Furnas
We present a 2x2 Lax representation for discrete circular nets of constant negative Gauß curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete…
A discrete parametrized surface theory in R^3
Tim Hoffmann, Andrew O. Sageman-Furnas, Max Wardetzky
We propose a discrete surface theory in that unites the most prevalent versions of discrete special parametrizations. This theory encapsulates a large class of discre…