Fischer-Koch Tower (translation-invariant)
Fischer-Koch Tower (translation-invariant) is a singly periodic minimal surface, given by a Weierstrass representation, 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
- 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.sfk_fkt_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.
- W. Fischer, E. Koch, "Spanning minimal surfaces", Phil. Trans. R. Soc. Lond. A 354 (1996) 2105-2142;
- M. Weber, https://minimalsurfaces.blog/ -- notebooks "Fischer-Koch Translational", "Fischer-Koch-Freese" (after R. Freese), "Singly Periodic Torus with One Catenoid and Two Annular Ends", "Translation Invariant Torus with Two Enneper and Two Annular Ends" (research/msblog_harvest/singly_periodic.json);
- H. Karcher, "Embedded minimal surfaces derived from Scherk's examples", Manuscripta Math. 62 (1988);
- B. C. Carlson, Numer. Algorithms 10 (1995) 13-26 (R_F).