The computer-aided discovery of new embedded minimal surfaces

@article{Hoffman1987TheCD,
  title={The computer-aided discovery of new embedded minimal surfaces},
  author={David Hoffman and Henri Matisse},
  journal={The Mathematical Intelligencer},
  year={1987},
  volume={9},
  pages={8-21}
}
In 1984, Bill Meeks and I established the existence of an infinite family of complete embedded minimal surfaces in R 3. For each k > 0, there exists an example which is homeomorphic to a surface of genus k from which three points have been removed. Figure 30-1 is a picture of the genus-one example. The equations for this remarkable surface were established by Celsoe Costa in his thesis, but they were so complex that the underlying geometry was obscured. We used the computer to numerically… 

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We will survey what is known about minimal surfaces S ⊂ R 3, which are complete, embedded, and have finite total curvature: \(\int_s {|K|} dA < \infty \). The only classically known examples of such

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