Normalizing Topologically Minimal Surfaces II: Disks

Abstract

We show that a topologically minimal disk in a tetrahedron with index $n$ is either a normal triangle, a normal quadrilateral, or a normal helicoid with boundary length 4(n+1). This mirrors geometric results of Colding and Minicozzi.

References in corpus (2)

• Topological Index Theory for Surfaces in 3-Manifolds
• Normalizing Topologically Minimal Surfaces I: Global to Local Index

Cited by in corpus (5)

• Normalizing Topologically Minimal Surfaces I: Global to Local Index
• Normalizing Topologically Minimal Surfaces III: Bounded Combinatorics
• Admissible colourings of 3-manifold triangulations for Turaev-Viro type invariants
• On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three I - the Structure Theorem
• Generalized Heegaard splittings and the disk complex