Helicoidal Karcher-Scherk (twisted tower)
Helicoidal Karcher-Scherk (twisted tower) is a singly periodic minimal surface, given by a Weierstrass representation, genus 0, immersed, with a rod group.
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def-weierstrass immersed implemented minimal minimal-periodic singly-periodic tradition-classical
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- singly periodic
- Genus
- 0
- Ends
- 0
- Embedding
- immersed
- Symmetry kind
- rod group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
No (g, dh) pair is stored: the shipped row is built by the dedicated mesher we.sptail_hks_mesh (a torus/branched-cover or multi-patch assembly); no elementary (g, dh) pair on a plane domain is stored in the code. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- H. Karcher, "Embedded minimal surfaces derived from Scherk's examples", Manuscripta Math. 62 (1988);
- H. F. Scherk (1835); A. Enneper (1864); M. Weber, https://minimalsurfaces.blog/ (6-Ended Scherk g0; Alternating Fence of Half-Catenoids, 2024; Fence of Catenoids; Helicoidal Karcher-Scherk; Periodic Enneper; Enneper-Scherk; Translation-Invariant Torus with 1 Enneper and 3 Annular Ends, notebook by Ramazan Yol, 2024).