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


Authors: Adam Coffman, Yifei Pan and Yuan Zhang
Journal: Trans. Amer. Math. Soc. 369 (2017), 4865-4887
MSC (2010): Primary 35J46; Secondary 30G20, 32Q65
DOI: https://doi.org/10.1090/tran/6845
Published electronically: February 13, 2017
MathSciNet review: 3632553
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish elliptic regularity for nonlinear, inhomogeneous
Cauchy-Riemann equations under weak 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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Additional Information

Adam Coffman
Affiliation: Department of Mathematical Sciences, Indiana University - Purdue University Fort Wayne, 2101 E. Coliseum Boulevard, Fort Wayne, Indiana 46805-1499
Email: CoffmanA@ipfw.edu

Yifei Pan
Affiliation: College of Mathematics and Information Sciences, Jiangxi Normal University, Nanchang, People’s Republic of China
Email: Pan@ipfw.edu

Yuan Zhang
Affiliation: Department of Mathematical Sciences, Indiana University - Purdue University Fort Wayne, 2101 E. Coliseum Boulevard, Fort Wayne, Indiana 46805-1499
Email: ZhangYu@ipfw.edu

DOI: https://doi.org/10.1090/tran/6845
Received by editor(s): February 26, 2015
Received by editor(s) in revised form: March 2, 2015, and July 27, 2015
Published electronically: February 13, 2017
Additional Notes: The first author is the corresponding author
This paper was presented to the American Mathematical Society at the Spring 2015 Central Sectional Meeting in East Lansing, Michigan
Article copyright: © Copyright 2017 American Mathematical Society