Continuous Solutions of Nonlinear Cauchy-Riemann equations and Pseudoholomorphic Curves in Normal Coordinates
Transactions of the American Mathematical Society
American Mathematical Society
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal 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.
Analysis | Geometry and Topology | Mathematics
Adam Coffman, Yifei Pan, and Yuan Zhang (2017).
Continuous Solutions of Nonlinear Cauchy-Riemann equations and Pseudoholomorphic Curves in Normal Coordinates. Transactions of the American Mathematical Society.369 (7), 4865-4887. American Mathematical Society.