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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Introduces framed Beltrami-Vekua normal form for elliptic systems and proves its pseudo-analytic mass is invariant under recombination and quasiconformal maps, reducing every such equation to the μ=0 case with equal mass.
Proves that re-normalizing the Beltrami-Vekua normal form after any pointwise invertible real-linear substitution of unknowns returns to the gauge orbit of the original equation via the explicit gauge ilde{\varphi}=-iλ/(ϕ-ψ).
citing papers explorer
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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.
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The Framed Beltrami-Vekua Normal Form and its Pseudo-Analytic Mass
Introduces framed Beltrami-Vekua normal form for elliptic systems and proves its pseudo-analytic mass is invariant under recombination and quasiconformal maps, reducing every such equation to the μ=0 case with equal mass.
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The Absorption Theorem for the Beltrami-Vekua Normal Form
Proves that re-normalizing the Beltrami-Vekua normal form after any pointwise invertible real-linear substitution of unknowns returns to the gauge orbit of the original equation via the explicit gauge ilde{\varphi}=-iλ/(ϕ-ψ).