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

2014/10/06 by Adam Coffman, Yifei Pan, Coffman, Adam +3
Mathematics · #30G20 #32Q65 #35J46 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.AP #math.CV #msc:30G20 #msc:32Q65 #msc:35J46

paper · pdf · doi:10.48550/arxiv.1410.1582

Version 3 with new Section 4.2 based on suggestions of referee. Accepted to appear in Transactions AMS

openalex publication_date 2014/10/06 · arxiv created 2015/10/02 · arxiv updated 2015/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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