Previous |  Up |  Next

Article

Title: The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains (English)
Author: Kim, Hyeseon
Author: Yamamori, Atsushi
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 68
Issue: 3
Year: 2018
Pages: 611-631
Summary lang: English
.
Category: math
.
Summary: We consider a certain class of unbounded nonhyperbolic Reinhardt domains which is called the twisted Fock-Bargmann-Hartogs domains. By showing Cartan's linearity theorem for our unbounded nonhyperbolic domains, we give a complete description of the automorphism groups of twisted Fock-Bargmann-Hartogs domains. (English)
Keyword: holomorphic automorphism group
Keyword: Bergman kernel
Keyword: Reinhardt domain
MSC: 32A07
MSC: 32A25
MSC: 32M05
idZBL: Zbl 06986960
idMR: MR3851879
DOI: 10.21136/CMJ.2018.0551-16
.
Date available: 2018-08-09T13:09:15Z
Last updated: 2020-10-05
Stable URL: http://hdl.handle.net/10338.dmlcz/147356
.
Reference: [1] Ahn, H., Byun, J., Park, J.-D.: Automorphisms of the Hartogs type domains over classical symmetric domains.Int. J. Math. 23 (2012), 1250098, 11 pages. Zbl 1248.32001, MR 2959444, 10.1142/S0129167X1250098X
Reference: [2] Bi, E., Feng, Z., Tu, Z.: Balanced metrics on the Fock-Bargmann-Hartogs domains.Ann. Global Anal. Geom. 49 (2016), 349-359. Zbl 1355.32004, MR 3510521, 10.1007/s10455-016-9495-3
Reference: [3] D'Angelo, J. P.: An explicit computation of the Bergman kernel function.J. Geom. Anal. 4 (1994), 23-34. Zbl 0794.32021, MR 1274136, 10.1007/BF02921591
Reference: [4] Engliš, M., Zhang, G.: On a generalized Forelli-Rudin construction.Complex Var. Elliptic Equ. 51 (2006), 277-294. Zbl 1202.32017, MR 2200983, 10.1080/17476930500515017
Reference: [5] Huo, Z.: The Bergman kernel on some Hartogs domains.J. Geom. Anal. 27 (2017), 271-299. Zbl 1367.32004, MR 3606552, 10.1007/s12220-016-9681-3
Reference: [6] Ishi, H., Kai, C.: The representative domain of a homogeneous bounded domain.Kyushu J. Math. 64 (2010), 35-47. Zbl 1195.32009, MR 2662658, 10.2206/kyushujm.64.35
Reference: [7] Jarnicki, M., Pflug, P.: First Steps in Several Complex Variables: Reinhardt Domains.EMS Textbooks in Mathematics, European Mathematical Society, Zürich (2008). Zbl 1148.32001, MR 2396710, 10.4171/049
Reference: [8] Jarnicki, M., Pflug, P.: Invariant Distances and Metrics in Complex Analysis.De Gruyter Expositions in Mathematics 9, Walter de Gruyter, Berlin (2013). Zbl 1273.32002, MR 3114789, 10.1515/9783110253863
Reference: [9] Kim, H., Ninh, V. T., Yamamori, A.: The automorphism group of a certain unbounded non-hyperbolic domain.J. Math. Anal. Appl. 409 (2014), 637-642. Zbl 1307.32017, MR 3103183, 10.1016/j.jmaa.2013.07.007
Reference: [10] Kim, H., Yamamori, A.: An application of a Diederich-Ohsawa theorem in characterizing some Hartogs domains.Bull. Sci. Math. 139 (2015), 737-749. Zbl 1351.32032, MR 3407513, 10.1016/j.bulsci.2014.11.007
Reference: [11] Kim, H., Yamamori, A., Zhang, L.: Invariant metrics on unbounded strongly pseudoconvex domains with non-compact automorphism group.Ann. Global Anal. Geom. 50 (2016), 261-295. Zbl 1360.32008, MR 3554375, 10.1007/s10455-016-9511-7
Reference: [12] Kodama, A.: On the holomorphic automorphism group of a generalized complex ellipsoid.Complex Var. Elliptic Equ. 59 (2014), 1342-1349. Zbl 1300.32001, MR 3210305, 10.1080/17476933.2013.845177
Reference: [13] Ligocka, E.: On the Forelli-Rudin construction and weighted Bergman projections.Stud. Math. 94 (1989), 257-272. Zbl 0688.32020, MR 1019793, 10.4064/sm-94-3-257-272
Reference: [14] Loi, A., Zedda, M.: Balanced metrics on Cartan and Cartan-Hartogs domains.Math. Z. 270 (2012), 1077-1087. Zbl 1239.53093, MR 2892939, 10.1007/s00209-011-0842-6
Reference: [15] Lu, Q.: On the representative domain.Several Complex Variables Proc. 1981 Hangzhou Conf., Birkhäuser, Boston (1984), 199-211. Zbl 0564.32014, MR 0897597, 10.1007/978-1-4612-5296-2_22
Reference: [16] Ning, J., Zhang, H., Zhou, X.: Proper holomorphic mappings between invariant domains in $\Bbb C^n$.Trans. Am. Math. Soc. 369 (2017), 517-536. Zbl 1351.32003, MR 3557783, 10.1090/tran/6690
Reference: [17] Rong, F.: On automorphism groups of generalized Hua domains.Math. Proc. Camb. Philos. Soc. 156 (2014), 461-472. Zbl 1290.32020, MR 3181635, 10.1017/S0305004114000048
Reference: [18] Rong, F.: On automorphisms of quasi-circular domains fixing the origin.Bull. Sci. Math. 140 (2016), 92-98. Zbl 1338.32020, MR 3446951, 10.1016/j.bulsci.2015.02.001
Reference: [19] Roos, G.: Weighted Bergman kernels and virtual Bergman kernels.Sci. China Ser. A 48 (2005), Suppl., 225-237. Zbl 1125.32001, MR 2156503, 10.1007/BF02884708
Reference: [20] Springer, G.: Pseudo-conformal transformations onto circular domains.Duke Math. J. 18 (1951), 411-424. Zbl 0043.30401, MR 0041233, 10.1215/S0012-7094-51-01832-7
Reference: [21] Tsuboi, T.: Bergman representative domains and minimal domains.Jap. J. Math. 29 (1959), 141-148. Zbl 0097.06703, MR 0121504, 10.4099/jjm1924.29.0_141
Reference: [22] Tu, Z., Wang, L.: Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domains.J. Math. Anal. Appl. 419 (2014), 703-714. Zbl 1293.32002, MR 3225398, 10.1016/j.jmaa.2014.04.073
Reference: [23] Tu, Z., Wang, L.: Rigidity of proper holomorphic mappings between equidimensional Hua domains.Math. Ann. 363 (2015), 1-34. Zbl 1330.32007, MR 3394371, 10.1007/s00208-014-1136-1
Reference: [24] Yamamori, A.: A remark on the Bergman kernels of the Cartan-Hartogs domains.C. R., Math. Acad. Sci. Paris 350 (2012), 157-160. Zbl 1239.32002, MR 2891103, 10.1016/j.crma.2012.01.005
Reference: [25] Yamamori, A.: The Bergman kernel of the Fock-Bargmann-Hartogs domain and the polylogarithm function.Complex Var. Elliptic Equ. 58 (2013), 783-793. Zbl 1272.32002, MR 3170660, 10.1080/17476933.2011.620098
Reference: [26] Yamamori, A.: Automorphisms of normal quasi-circular domains.Bull. Sci. Math. 138 (2014), 406-415. Zbl 1288.32003, MR 3206476, 10.1016/j.bulsci.2013.10.002
Reference: [27] Yamamori, A.: A generalization of the Forelli-Rudin construction and deflation identities.Proc. Am. Math. Soc. 143 (2015), 1569-1581. Zbl 1321.32004, MR 3314070, 10.1090/S0002-9939-2014-12317-3
Reference: [28] Yamamori, A.: Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan's linearity theorem and explicit Bergman kernel.Tohoku Math. J. 69 (2017), 239-260. Zbl 06775254, MR 3682165, 10.2748/tmj/1498269625
Reference: [29] Yin, W.: The Bergman kernels on Cartan-Hartogs domains.Chin. Sci. Bull. 44 (1999), 1947-1951. Zbl 1039.32502, MR 1752411, 10.1007/BF02887114
Reference: [30] Zedda, M.: Berezin-Engliš' quantization of Cartan-Hartogs domains.J. Geom. Phys. 100 (2016), 62-67. Zbl 1330.53104, MR 3435762, 10.1016/j.geomphys.2015.11.002
Reference: [31] Zhang, L.: Bergman kernel function on Hua construction of the second type.Sci. China Ser. A 48 (2005), Suppl., 400-412. Zbl 1128.32002, MR 2156520, 10.1007/BF02884724
.

Files

Files Size Format View
CzechMathJ_68-2018-3_3.pdf 396.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo