| Title:
|
Construction of stationary discs for perturbations of decoupled submanifolds in $\mathbb{C}^4$ (English) |
| Author:
|
Al Masri, Mohammad Tarek |
| Author:
|
Bertrand, Florian |
| Author:
|
Mchaimech, Jad |
| Author:
|
Oueidat, Lea |
| Author:
|
Zoghaib, Hadi |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
61 |
| Issue:
|
5 |
| Year:
|
2025 |
| Pages:
|
175-186 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct generalized stationary discs to perturbations of decoupled real submanifolds of codimension $2$ in $\mathbb{C}^4$. (English) |
| Keyword:
|
stationary discs |
| Keyword:
|
CR submanifolds |
| MSC:
|
32V40 |
| idZBL:
|
Zbl 08162263 |
| DOI:
|
10.5817/AM2025-5-175 |
| . |
| Date available:
|
2026-01-23T11:28:31Z |
| Last updated:
|
2026-03-16 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153282 |
| . |
| Reference:
|
[1] Bertrand, F., Blanc-Centi, L.: Stationary holomorphic discs and finite jet determination problems.Math. Ann. 358 (2014), 477–509. MR 3158006, 10.1007/s00208-013-0972-8 |
| Reference:
|
[2] Bertrand, F., Blanc-Centi, L., Meylan, F.: Stationary discs and finite jet determination for non-degenerate generic real submanifolds.Adv. Math. 343 (2019), 910–934. MR 3891986, 10.1016/j.aim.2018.12.005 |
| Reference:
|
[3] Bertrand, F., Della Sala, G.: Stationary discs for smooth hypersurfaces of finite type and finite jet determination.J. Geom. Anal. 25 (2015), 2516–2545. MR 3427136, 10.1007/s12220-014-9524-z |
| Reference:
|
[4] Bertrand, F., Della Sala, G.: Riemann-Hilbert problems with constraints.Proc. Amer. Math. Soc. 147 (2019), 2123–2131. MR 3937687, 10.1090/proc/14390 |
| Reference:
|
[5] Bertrand, F., Della Sala, G., Lamel, B.: Jet determination of smooth CR automorphisms and generalized stationary discs.Math. Z. 294 (2020), 1611–1634. MR 4074052, 10.1007/s00209-019-02330-9 |
| Reference:
|
[6] Blanc-Centi, L.: Stationary discs glued to a Levi non-degenerate hypersurface.Trans. Amer. Math. Soc. 361 (2009), 3223–3239. MR 2485424, 10.1090/S0002-9947-08-04737-5 |
| Reference:
|
[7] Ebenfelt, P., Lamel, B., Zaitsev, D.: Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case.Geom. Funct. Anal. 13 (2003), 546–573. MR 1995799, 10.1007/s00039-003-0422-y |
| Reference:
|
[8] Forstnerič, F.: Analytic disks with boundaries in a maximal real submanifold of $\mathbb{C}^2$.Ann. Inst. Fourier 37 (1987), 1–44. 10.5802/aif.1076 |
| Reference:
|
[9] Globevnik, J.: Perturbation by analytic discs along maximal real submanifolds of $\mathbb{C}^N$.Math. Z. 217 (1994), 287–316. 10.1007/BF02571946 |
| Reference:
|
[10] Globevnik, J.: Perturbing analytic discs attached to maximal real submanifolds of $\mathbb{C}^N$.Indag. Math. (N.S.) 7 (1996), 37–46. 10.1016/0019-3577(96)88655-1 |
| Reference:
|
[11] Hill, C.D., Taiani, G.: Families of analytic discs in $\mathbb{C}^n$ with boundaries on a prescribed CR submanifold.Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 5 (1978), 327–380. |
| Reference:
|
[12] Huang, X.: A non-degeneracy property of extremal mappings and iterates of holomorphic self-mappings.Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 21 (1994), 399–419. |
| Reference:
|
[13] Lempert, L.: La métrique de Kobayashi et la représentation des domaines sur la boule.Bull. Soc. Math. France 109 (1981), 427–474. 10.24033/bsmf.1948 |
| Reference:
|
[14] Tumanov, A.: Extremal discs and the regularity of CR mappings in higher codimension.Amer. J. Math. 123 (2001), 445–473. MR 1833148, 10.1353/ajm.2001.0022 |
| Reference:
|
[15] Tumanov, A.: Stationary discs and finite jet determination for CR mappings in higher codimension.Adv. Math. 371 (2020), 11 pp. MR 4116100, 10.1016/j.aim.2020.107254 |
| Reference:
|
[16] Vekua, N.P.: Systems of singular integral equations.Noordhoff, Groningen, 1967, 216 pp. |
| . |
