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

Adam Coffman; Yifei Pan; Yuan Zhang

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

Complex Variables 2015-10-05 v3 Analysis of PDEs

Authors: Adam Coffman , Yifei Pan , Yuan Zhang

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.

Keywords

cauchy-riemann equations elliptic regularity pseudoholomorphic curves almost complex structures normal coordinates continuous solutions counterexample

Cite

@article{arxiv.1410.1582,
  title  = {Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates},
  author = {Adam Coffman and Yifei Pan and Yuan Zhang},
  journal= {arXiv preprint arXiv:1410.1582},
  year   = {2015}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

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