Horgan surface
From HandWiki
In differential geometry, Horgan's surface is a near-minimal surface.
David Hoffman and Hermann Karcher explored complete, embedded, and finite total curvature minimal surfaces. They considered a genus 2 variation of the Costa surface, with the same symmetries, one planar end, and two catenoid ends[1]. While computer modeling of the surface looked promising, the period problem cannot be solved, and there does not exist any minimal surface with this symmetry [2][3].
Hoffman and Karcher named the simulated surface after John Horgan, as a response to his claim that the use of rigorous mathematical proofs was becoming obsolete[4]: they saw it as a case for the necessity of rigorous proof. Horgan appear to have taken the naming well[5].
External Links
References
- ↑ Hoffman, David; Karcher, Hermann (1995-08-09), Complete embedded minimal surfaces of finite total curvature, arXiv, doi:10.48550/arXiv.math/9508213, arXiv:math/9508213, http://arxiv.org/abs/math/9508213, retrieved 2026-03-21
- ↑ Weber, M. (1998). On the Horgan minimal non-surface. Calculus of Variations and Partial Differential Equations, 7(4), 373-379.
- ↑ Weber, M., & Wolf, M. (2002). Teichmüller theory and handle addition for minimal surfaces. Annals of mathematics, 713-795.
- ↑ Horgan J. (October 1993) The Death of Proof (Trends in Mathematics). Scientific American, Vol. 269, No. 4, pp. 92–103.
- ↑ Horgan, John. "The Horgan Surface and the Death of Proof" (in en). https://www.scientificamerican.com/blog/cross-check/the-horgan-surface-and-the-death-of-proof/.
 | ||
 |  |
