Wavy Enneper
Wavy Enneper is a minimal surface, given by a Weierstrass representation, immersed.
Open Wavy Enneper in the interactive viewer →
aperiodic def-weierstrass immersed implemented minimal tradition-classical
Properties
- Family
- minimal
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
Enneper surface modified so waves develop around its boundary and can travel around it: a finite total curvature minimal immersion of the once-punctured sphere with k-fold symmetry (the exhibit shows the 3-fold case), from Karcher's Tokyo notes.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- The 3DXM Consortium, "Wavy Enneper", "Karcher JD Saddle Tower" and "Karcher JE Saddle Tower" exhibits, https://virtualmathmuseum.org/
- H. Karcher, "Construction of minimal surfaces", in "Surveys in Geometry", Univ. of Tokyo, 1989, and Lecture Notes No. 12, SFB 256,
- Bonn, 1989, pp. 1-96 -- the Enneper-end language and the doubly periodic examples (section 3.3).
- H. Karcher, "Embedded minimal surfaces derived from Scherk's examples", Manuscripta Math. 62 (1988) 83-114 -- the JD/JE tower families.
- - the exact exhibit data (Gauss map, dh, parameter ranges) followed here.
- A. Enneper (1864) -- the base surface the waves ride on.
- The 3DXM Consortium, 'Wavy Enneper Surface', Virtual Math Museum, virtualmathmuseum.org (local mirror: vmm/book/surface/ch010_wavy_enneper.md).
- H. Karcher, 'Construction of minimal surfaces', Surveys in Geometry, Univ. of Tokyo, 1989, and Lecture Notes No. 12, SFB 256, Bonn (1989) 1-96 (the 'Tokyo notes' the mirrored pages cite for their formulas).