Abstract |
We prove that there is only one way to 'desingularize' the intersection of
two planes in space and to obtain a periodic minimal surface as a result.
The proof is mostly an exercise in, and an introduction to, basic
Teichmüller theory: we translate the geometry of minimal surface in
space into a statement about a moduli space of flat structures on Riemann
surfaces, and then study deformation theory and degenerations in this
moduli space to prove the result. We remark on the general (non-periodic)
case.
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