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Richmond surface

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Richmond surface for m=2.

In differential geometry, a Richmond surface is a minimal surface first described by Herbert William Richmond in 1904. [1] It is a family of surfaces with one planar end and one Enneper surface-like self-intersecting end.

It has Weierstrass–Enneper parameterization . This allows a parametrization based on a complex parameter as

The associate family of the surface is just the surface rotated around the z-axis.

Taking m = 2 a real parametric expression becomes:[2]

References

  1. ^ Jesse Douglas, Tibor Radó, The Problem of Plateau: A Tribute to Jesse Douglas & Tibor Radó, World Scientific, 1992 (p. 239-240)
  2. ^ John Oprea, The Mathematics of Soap Films: Explorations With Maple, American Mathematical Soc., 2000