Moduli of the Sourceless Framed Beltrami-Vekua Normal Form

Key points

It reduced the sourceless Beltrami-Vekua equation on a simply connected domain with boundary to a minimal form on the unit disk and precisely characterized the remaining symmetries.
When the coefficient field has no zeros, the pair ϑ and K completely classifies the equation, and it also determined the range of possible invariants.
In phase-integrable regions containing zeros, it expanded the classification data to the three quantities ϑ, dη, and d⋆η, separating vortex charge from the remaining phase curvature.
It explicitly constructed inequivalent equations with the same mass and charge, showing that those two numbers cannot capture the infinite-dimensional classification space.
Multiply connected domains require additional period data, and complete classification remains open for rough measurable coefficients or zeros that are not phase-integrable.

External research summaries. These are not HDATF publications or measured product results.