Chen-Gackstatter Surface
Chen-Gackstatter Surface is a minimal surface, given by a Weierstrass representation, genus 1, 1 end, self-intersecting.
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aperiodic complete-finite-total-curvature def-weierstrass implemented minimal self-intersecting tradition-classical
Properties
- Family
- minimal
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- not periodic
- Genus
- 1
- Ends
- 1
- Embedding
- self-intersecting
- Orientable
- yes
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
No (g, dh) pair is stored: the shipped immersion is a closed form in Weierstrass elliptic functions (zeta, wp, wp') on the square torus (math_art/minsurf/parametric.py) -- outside the elementary expression language. 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. C. Chen and F. Gackstatter, 'Elliptische und hyperelliptische Funktionen und vollstandige Minimalflachen vom Enneperschen Typ', Math. Ann. 259 (1982).
- C. C. Chen, F. Gackstatter, Math. Ann. 259 (1982) 359-369; M. Weber (mirror: minsurf ch058): total curvature -4pi(g+1) for the genus-g member, 'the largest possible value for its genus'.