Breiner-Kleene Spiral Helicoid
Breiner-Kleene Spiral Helicoid is a minimal surface, given by a Weierstrass representation, immersed.
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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
Bjorling's problem: the minimal surface through a given curve with a given normal along it. Embedded minimal surfaces invariant under a screw motion composed with a homothety: bent helicoids following a logarithmically spiraling helix, embedded in an invariant tube around it (Breiner-Kleene 2014).
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- R. Schoen / Lopez & Ros (1991) on the Lopez-Ros deformation; H. F. Scherk (1835) for the base Scherk surface; the decorated-Enneper symmetrization follows M. Weber's repository, https://minimalsurfaces.blog/ (Enneper with n Catenoids).
- M. Weber, 'Breiner-Kleene Surface', minimalsurfaces.blog (local mirror: minsurf/book/.../ch005_breiner_kleene_surface.md).
- C. Breiner and S. Kleene, 'Logarithmically spiraling helicoids', arXiv:1404.6996 (2014).