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Partial integrability of almost complex structures and the existence of solutions for quasilinear Cauchy–Riemann equations
We study the local solvability of the system of quasilinear Cauchy-Riemann equations for d unknown functions in n complex variables, which is a system of elliptic type and overdetermined if n ≥ 2. We consider an associated almost complex structure on ރ n+d and its partial integrability and prove by …