Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates
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- by Adam Coffman, Yifei Pan and Yuan Zhang PDF
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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.References
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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
- MR Author ID: 607214
- ORCID: 0000-0002-1437-7525
- Email: CoffmanA@ipfw.edu
- Yifei Pan
- Affiliation: College of Mathematics and Information Sciences, Jiangxi Normal University, Nanchang, People’s Republic of China
- MR Author ID: 213987
- 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
- MR Author ID: 799458
- Email: ZhangYu@ipfw.edu
- 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 - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 4865-4887
- MSC (2010): Primary 35J46; Secondary 30G20, 32Q65
- DOI: https://doi.org/10.1090/tran/6845
- MathSciNet review: 3632553