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,A note on elliptic first order systems in the plane and the Vekua equation with structure polynomialX 2 +βX+α, preprint
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This note deals with the following problem: under which conditions can elliptic first order systems in the plane be complex-rewritten as a parameter-depending Vekua-type equation?
fields
math.CV 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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 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).