not yet built
Dihedralized Wohlgemuth with Handle
Dihedralized Wohlgemuth with Handle is a minimal surface, given by a Weierstrass representation, immersed.
Open Dihedralized Wohlgemuth with Handle in the interactive viewer →
aperiodic def-weierstrass immersed minimal not-implemented tradition-classical
Properties
- Family
- minimal
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
The attempted k >= 3 dihedral symmetrization of Wohlgemuth's genus-3 handle surface. Its failure questions the folklore that a surface existing for some dihedral order k exists for all larger k.
Not yet built
This surface is catalogued but not yet built by the extension, so it has no mesh or thumbnail here.
Sources
Not transcribed. The record exists to state that the surface is absent and why; a fabricated equation would be worse than a null.
- M. Weber, 'Wohlgemuth's Second Surface (which documents the failed dihedralization)', minimalsurfaces.blog (local mirror: minsurf/book/.../ch418_wohlgemuths_second_surface.md).
- M. Weber, 'Non-Existent Surfaces (section index)', minimalsurfaces.blog (local mirror: minsurf/book/.../ch061_non_existent_surfaces.md).
- M. Wohlgemuth, 'Minimal surfaces of higher genus with finite total curvature', Arch. Rational Mech. Anal. 137 (1997) 1-25 (the existing k = 2 surface).