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arXiv · 1410.1582

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

Adam Coffman·Yifei Pan·Yuan Zhang
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Abstract

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.

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Adam Coffman, Yifei Pan, Yuan Zhang. 2014-10-06. Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates. https://arxiv.org/abs/1410.1582

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