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math.DG2025
Discrete curve theory in space forms: planar elastic and area-constrained elastic curves
Tim Hoffmann, Jannik Steinmeier, Gudrun Szewieczek
We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equatio…
math.DG2024
Isothermic nets with spherical parameter lines from discrete holomorphic maps
Tim Hoffmann, Gudrun Szewieczek
We prove that all discrete isothermic nets with a family of planar or spherical lines of curvature can be obtained from special discrete holomorphic maps via lifted-folding. This n…