Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates

Coffman, Adam; Pan, Yifei; Zhang, Yuan

doi:10.1090/tran/6845

Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates
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by Adam Coffman, Yifei Pan and Yuan Zhang PDF

Trans. Amer. Math. Soc. 369 (2017), 4865-4887 Request permission

Abstract:

We establish elliptic regularity for nonlinear, inhomogeneous Cauchy-Riemann equations under weak assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the solution set can be explicitly calculated. The methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost complex structures.

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