COMMENTS ON: CONTINUOUS SOLUTIONS OF NONLINEAR CAUCHY-RIEMANN EQUATIONS AND

PSEUDOHOLOMORPHIC CURVES IN NORMAL COORDINATES

ADAM COFFMAN, YIFEI PAN, YUAN ZHANG

Last update: May 15, 2023.

1. Errata

On p. 4873, the RHS of Equation (3.5) should have the z-derivative, \frac{∂}{∂z} (κ(|z|)), to match the LHS. This correction does not affect any later conclusions, and that term is zero when evaluated in the next step.

2. Updates

There are reviews in MR and Zbl for this article: [CPZ].

Our PFW contact information has changed. The email addresses have all changed from ipfw.edu to pfw.edu. The Corresponding Author’s current home page can be found at:

  http://users.pfw.edu/CoffmanA/

3. Citations

The article is cited in these papers: [FPZ], [PY].

References

[CPZ] A. Coffman, Y. Pan, and Y. Zhang, Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates, Transactions of the AMS (7) 369 (2017), 4865–4887. MR 3632553; Zbl 1375.35152

[FPZ] M. Fassina, Y. Pan, and Y. Zhang, A remark on optimal data spaces for classical solutions of \overline{∂}, Rocky Mountain J. Math. (2) 52 (2022), 499–506. MR 4422952; Zbl 07555150

[PY] Y. Pan and Y. Yan, Examples of twice differentiable functions with continuous Laplacian and unbounded Hessian, Collect. Math. (2) 75 (2024), 453–479. MR 4724123; Zbl 07832891

Department of Mathematical Sciences, Purdue University Fort Wayne, 2101 E. Coliseum Blvd., Fort Wayne, IN 46805-1499

   Email address: CoffmanA@pfw.edu