COMMENTS ON:

ANALYTIC STABILITY OF THE CR CROSS-CAP

ADAM COFFMAN

Last update: June 7, 2023.

1. Updates

There are reviews in MR and Zbl for this article: [C_{3}] and the reference [Coffman 2006]: [C_{2}], and the reference [Coffman 1997] has also been indexed in MR: [C_{1}].

My contact information has changed, and the web address printed at the end of the article and appearing on the PJM web page is now obsolete. My current home page can be found at:

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

2. Citations

The article is cited in these papers: [B], [GL], [Gong-St], [Gupta-Sh], [HY], [KZ_{1}], [KZ_{2}], [SZ], [Z].

As mentioned at the end of the paper, there was an earlier version, entitled Formal stability of the CR cross-cap, which was circulated as a preprint and remains posted on my web site. Before the appearance of the published version [C_{3}], the earlier version was cited by a few of my own papers as well as the following: [BER], [BRZ].

References

[BER] M. S. Baouendi, P. Ebenfelt, and L. Preiss Rothschild, Local geometric properties of real submanifolds in complex space, Bull. AMS (N.S.) (3) 37 (2000), 309–336. MR 1754643 (2001a:32043), Zbl 0955.32027.

[BRZ] M. S. Baouendi, L. Preiss Rothschild, and D. Zaitsev, Equivalences of real submanifolds in complex space, J. Differential Geom. (2) 59 (2001), 301–351. MR 1908985 (2003k:32051), Zbl 1037.32030.

[B] V. Burcea, Real submanifolds in complex spaces, Acta Math. Sin. (1) 33 (2017), 1–20. MR 3581602, Zbl 1359.32029.

[C_{1}] A. Coffman, Enumeration and Normal Forms of Singularities in Cauchy-Riemann

Structures, dissertation, University of Chicago, 1997. MR 2716702.

[C_{2}] A. Coffman, CR singularities of real threefolds in ℂ^{4}, Advances in Geometry (1) 6

(2006), 109–137. MR 2242865 (2007d:32033), Zbl 1120.32024.

[C_{3}] A. Coffman, Analytic stability of the CR cross-cap, Pacific J. Math. (2) 226 (2006),

221–258. MR 2247863 (2007j:32038), Zbl 1123.32018.

[GL] X. Gong and J. Lebl, Normal forms for CR singular codimension-two Levi-flat submanifolds, Pacific J. Math. (1) 275 (2015), 115–165. MR 3336931, Zbl 1376.32037.

[Gong-St] X. Gong and L. Stolovitch, Real submanifolds of maximum complex tangent space at a CR singular point, I, Invent. Math. (2) 206 (2016), 293–377. MR 3570294, Zbl 1358.32018.

[Gupta-Sh] P. Gupta and R. Shafikov, Polynomially convex embeddings of even-dimensional compact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 21 (2020), 1659–1666. MR 4288643, Zbl 1480.32002.

[HY] X. Huang and W. Yin, A codimension two CR singular submanifold that is formally equivalent to a symmetric quadric, Int. Math. Res. Not. (15) 2009 (2009), 2789–2828. MR 2525841 (2010f:32038), Zbl 1182.32014.

[KZ_{1}] I. Kossovskiy and D. Zaitsev, Convergent normal form and canonical connection for hypersurfaces of finite type in ℂ^{2}, Advances in Math. 281 (2015), 670–705. MR 3366850, Zbl 1320.53064.

[KZ_{2}] I. Kossovskiy and D. Zaitsev, Convergent normal form for real hypersurfaces at a generic Levi-degeneracy, J. Reine Angew. Math. 749 (2019), 201–225. MR 3935903, Zbl 1421.32040.

[SZ] L. Stolovitch and Z. Zhao, Geometry of hyperbolic Cauchy-Riemann singularities and KAM-like theory for holomorphic involutions, Math. Ann. (1–2) 386 (2023), 587–672. MR 4585158, Zbl 7686091.

[Z] D. Zaitsev, Formal and finite order equivalences, Math. Z. (3–4) 269 (2011), 687–696. MR 2860259 (2012j:32037), Zbl 1239.32007.

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

Email address: CoffmanA@pfw.edu