Lopez-Martin Slab Surface
Lopez-Martin Slab Surface is a singly periodic minimal surface, given by a Weierstrass representation, immersed, with a rod group.
Open Lopez-Martin Slab Surface in the interactive viewer →
def-weierstrass immersed implemented minimal minimal-periodic non-orientable singly-periodic tradition-classical
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- singly periodic
- Ends
- 0
- Embedding
- immersed
- Orientable
- no
- Symmetry kind
- rod group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
Translation invariant minimal surface with planar ends, neither embedded (self-intersection along the z-axis only) nor orientable; solves a Plateau problem in a wedge of a slab, and arises from the translation invariant helicoid-with-handle family when its vertical period condition is left unsolved.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- B. Riemann (1867) and F. J. Lopez, A. Ros, J. Differential Geom. 33 (1991) for the (never embedded) finite Riemann family; the symmetrized member follows M. Weber, minimalsurfaces.blog, "Symmetrized Finite Riemann".
- L. Henneberg (1875); R. Kusner, Bull. Amer. Math. Soc. 17 (1987) 291-295; F. J. Lopez, Duke Math. J. 71 (1993) 23-30 -- full citations in the weierstrass symtail engine block.
- H. Karcher, "Construction of minimal surfaces" (1989) for the symmetrization method (double Enneper, k-noid families);
- L. P. Jorge, W. H. Meeks III, Topology 22 (1983) for the k-noids; data after M. Weber, minimalsurfaces.blog ("Symmetrized Double Enneper", "k-Noids with Enneper Ends", "Antiprismatic k-Noids").
- M. Weber, 'Lopez-Martin Slab Surface', minimalsurfaces.blog (local mirror: minsurf/book/.../ch399_lopez_martin_slab_surface.md).
- F. J. Lopez and F. Martin, 'Minimal surfaces in a wedge of a slab' (the paper the mirrored page presents).