From Continuous to Discrete: the Example of Minimal Surfaces

John Sullivan
Technishche Universtitat Berlin

What is the least-area surface spanning a given boundary?
In the context of orientable surfaces, this problem is naturally dual to a maximum flow problem, and indeed a classical theorem of Federer says any least-area surface can be calibrated.
Solving the discrete minimum-cost circulation problem in an appropriate cell complex, we can get an arbitrarily good approximation to this continuous problem. But the surfaces we obtained are not discrete minimal in a useful sense.
We consider various notions from discrete differential geometry that can be used to get better discrete minimal surfaces.

Back to Graph Cuts and Related Discrete or Continuous Optimization Problems