Normalizing Topologically Minimal Surfaces III: Bounded Combinatorics

Abstract

We show that there are a finite number of possible pictures for a surface in a tetrahedron with local index $n$. Combined with previous results, this establishes that any topologically minimal surface can be transformed into one with a particular normal form with respect to any triangulation.

30 pages, 14 figures. This is the third and final paper of a series

References in corpus (2)

• Normalizing Topologically Minimal Surfaces II: Disks
• Normalizing Topologically Minimal Surfaces I: Global to Local Index