Comptes Rendus
Analyse et géométrie complexes
Canonical metrics on generalized Hartogs triangles
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 305-313.

This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles. On the other hand, we calculate the explicit expression for Rawnsley’s ε-function, and then we give the sufficient and necessary condition for the canonical metric to be balanced. As an application, we also find that there exist canonical metrics on generalized Hartogs triangles being both Kähler–Einstein and balanced.

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DOI : 10.5802/crmath.283
Classification : 32A25, 32Q15, 53C55

Enchao Bi 1 ; Zelin Hou 1

1 School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, P.R. China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Canonical metrics on generalized {Hartogs} triangles},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {305--313},
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     year = {2022},
     doi = {10.5802/crmath.283},
     language = {en},
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Enchao Bi; Zelin Hou. Canonical metrics on generalized Hartogs triangles. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 305-313. doi : 10.5802/crmath.283. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.283/

[1] Enchao Bi; Zhiming Feng; Zhenhan Tu Balanced metric on the Fock–Bargmann–Hartogs domains, Ann. Global Anal. Geom., Volume 49 (2016) no. 4, pp. 349-359 | MR | Zbl

[2] Enchao Bi; Guicong Su Balanced metric and Berezin quantization on Hartogs triangles, Ann. Mat. Pura Appl., Volume 200 (2021) no. 1, pp. 273-285 | MR | Zbl

[3] John S. Bland The Einstein-Kähler metric on {|z| 2 +|w| 2p <1}, Mich. Math. J., Volume 33 (1986) no. 2, pp. 209-220 | MR | Zbl

[4] Liwei Chen The L p boundedness of the Bergman projection for a class of bounded Hartogs domains, J. Math. Anal. Appl., Volume 448 (2017) no. 1, pp. 598-610 | DOI | MR | Zbl

[5] Shiu-Yuen Cheng; Shing-Tung Yau On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation, Commun. Pure Appl. Math., Volume 33 (1980) no. 4, pp. 507-544 | DOI | Zbl

[6] John P. D’Angelo An explicit computation of the Bergman kernel function, J. Geom. Anal., Volume 4 (1994) no. 1, pp. 23-34 | DOI | MR | Zbl

[7] Simon K. Donaldson Scalar curvature and projective embeddings, J. Differ. Geom., Volume 59 (2001) no. 3, pp. 479-522 | MR | Zbl

[8] Luke D. Edholm Bergman theory of certain generalized Hartogs triangles, Pac. J. Math., Volume 284 (2016) no. 2, pp. 327-342 | DOI | MR | Zbl

[9] Luke D. Edholm; Jeffery D. Mcneal The Bergman projection on fat Hartogs triangles: L p boundedness, Proc. Am. Math. Soc., Volume 144 (2015) no. 5, pp. 2185-2196 | DOI | MR | Zbl

[10] Miroslav Engliš Berezin quantization and reproducing kernels on complex domains, Trans. Am. Math. Soc., Volume 348 (1996) no. 2, pp. 411-479 | DOI | MR | Zbl

[11] Zhiming Feng; Zhenhan Tu Balanced metric on some Hartogs type domains over bounded symmetric domains, Ann. Global Anal. Geom., Volume 47 (2005) no. 4, pp. 305-333 | DOI | MR | Zbl

[12] Andrea Loi; Michela Zedda Balanced metrics on Hartogs domains, Abh. Math. Semin. Univ. Hamb., Volume 81 (2001) no. 1, pp. 69-77 | DOI | MR | Zbl

[13] Toshiki Mabuchi Stability of extremal Kähler manifolds, Osaka J. Math., Volume 41 (2004) no. 3, pp. 563-582 | Zbl

[14] Guicong Su Geometric properties of the pentablock, Complex Anal. Oper. Theory, Volume 14 (2020) no. 4, pp. 1-14 | MR | Zbl

[15] An Wang; Weiping Yin; Liyou Zhang; Guy Roos The Kähler–Einstein metric for some Hartogs domains over bounded symmetric domains, Sci. China, Volume 49 (2006) no. 9, pp. 1175-1210 | DOI | Zbl

[16] Paweł Zapałowski Proper holomorphic mappings between complex ellipsoids and generalized Hartogs triangles (2012) (https://arxiv.org/abs/1211.0786)

[17] Paweł Zapałowski Proper holomorphic mappings between generalized Hartogs triangles, Ann. Mat. Pura Appl., Volume 196 (2017) no. 3, pp. 1055-1071 | DOI | MR | Zbl

[18] Michela Zedda Canonical metric on Cartan–Hartogs domains, Int. J. Geom. Methods Mod. Phys., Volume 9 (2012) no. 1, 125011, 13 pages | MR | Zbl

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