not yet built
Catenoid with Handle
Catenoid with Handle is a minimal surface, given by a Weierstrass representation, immersed.
Open Catenoid 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 genus-1 catenoid: two catenoidal ends plus one handle. Ruled out by Schoen's characterization of the catenoid.
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, 'Translation Invariant Catenoid (which documents the failed inward-handle construction)', minimalsurfaces.blog (local mirror: minsurf/book/.../ch170_translation_invariant_catenoid.md).
- M. Weber, 'Non-Existent Surfaces (section index)', minimalsurfaces.blog (local mirror: minsurf/book/.../ch061_non_existent_surfaces.md).
- R. Schoen, 'Uniqueness, symmetry, and embeddedness of minimal surfaces', J. Differential Geom. 18 (1983) 791-809.