Translation-Invariant Costa
Translation-Invariant Costa is a singly periodic minimal surface, given by a Weierstrass representation, genus 1, 4 ends, 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
- 1
- Ends
- 4
- 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.stinv_costa_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.
- C. J. Costa (1984); D. Hoffman, W. H. Meeks III (1985); M. Weber, https://minimalsurfaces.blog/ -- the harvested notebooks (research/msblog_harvest/singly_periodic.json).
- H. Karcher, "Embedded minimal surfaces derived from Scherk's examples", Manuscripta Math. 62 (1988) 83-114;
- M. J. Callahan, D. Hoffman, W. H. Meeks III, "Embedded minimal surfaces with an infinite number of ends", Invent. Math. 96 (1989) 459-505;