A gauge-invariant 2-form Θ = |B|^2 / (1 - |μ|^2) dx dy yields a pseudo-analytic mass whose integral vanishes on analytic equations (B ≡ 0) and separates inequivalent classes on the disk.
Alayón-Solarz,Variable Elliptic Structures on the Plane: Transport Dynamics, Rigidity, and Function Theory, preprint
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The Pseudo-Analytic Mass of a Beltrami-Vekua Equation
A gauge-invariant 2-form Θ = |B|^2 / (1 - |μ|^2) dx dy yields a pseudo-analytic mass whose integral vanishes on analytic equations (B ≡ 0) and separates inequivalent classes on the disk.