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math.DG2024
Constant mean curvature surfaces from ring patterns: Geometry from combinatorics
Alexander I. Bobenko, Tim Hoffmann, Nina Smeenk
We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles.…
math.DG2024★ 3 cited
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…
math.DG2023★ 1 cited
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…