Karcher-Meeks-Rosenberg (doubly periodic)
Karcher-Meeks-Rosenberg (doubly periodic) is a doubly periodic minimal surface, given by a Weierstrass representation, genus 1, 4 ends, embedded, with a layer group.
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def-weierstrass doubly-periodic embedded implemented minimal minimal-periodic tradition-classical
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- doubly periodic
- Genus
- 1
- Ends
- 4
- Embedding
- embedded
- Symmetry kind
- layer group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
No (g, dh) pair is stored: the shipped row is built by the dedicated mesher we.dperiodic_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.
- M. J. Callahan, D. Hoffman, W. H. Meeks III, "Embedded minimal surfaces with an infinite number of ends", Invent. Math. 96 (1989) 459-505;
- M. Weber, https://minimalsurfaces.blog/ (Callahan-Hoffman-Meeks surfaces; the CHM-(1,1) notebook).