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Horgan surface

The Horgan minimal non-surface

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]

References

  1. ^ Hoffman, David; Karcher, Hermann (1995-08-09). "Complete embedded minimal surfaces of finite total curvature". arXiv:math/9508213.
  2. ^ Weber, Matthias (1 November 1998). "On the Horgan minimal non-surface". Calculus of Variations and Partial Differential Equations. 7 (4): 373–379. doi:10.1007/s005260050112.
  3. ^ Weber, M., & Wolf, M. (2002). Teichmüller theory and handle addition for minimal surfaces. Annals of mathematics, 713-795.
  4. ^ Horgan, John (1993). "The Death of Proof". Scientific American. 269 (4): 92–103. Bibcode:1993SciAm.269d..92H. doi:10.1038/scientificamerican1093-92. ISSN 0036-8733. JSTOR 24941653.
  5. ^ Horgan, John. "The Horgan Surface and the Death of Proof". Scientific American. Retrieved 2026-03-21.

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