Classification of free-boundary minimal disks in the tetragonal disphenoid

Classify all embedded free-boundary minimal disks contained in the tetragonal disphenoid T, beyond Smyth’s three disks constructed from the three normal quadrilaterals.

Background

The paper proves results for Smyth’s three embedded minimal disks in the tetragonal disphenoid T, identifying them with patches of the Schwarz P and D surfaces and determining their areas. It explicitly limits the theorem to those three disks and does not establish that they exhaust all free-boundary minimal disks in T.

A complete classification would determine whether additional free-boundary minimal disks exist in the same tetrahedron and would clarify the scope of the three-disk result.