Title

Continuous Solutions of Nonlinear Cauchy-Riemann equations and Pseudoholomorphic Curves in Normal Coordinates

Document Type

Article

Publication Date

7-2017

Publication Source

Transactions of the American Mathematical Society

Volume

369

Issue

7

Inclusive pages

4865-4887

DOI

http://dx.doi.org/10.1090/tran/6845

Publisher

American Mathematical Society

Peer Reviewed

yes

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.

Disciplines

Analysis | Geometry and Topology | Mathematics

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