Equality between the Bergman metric and Carathéodory metric
HTML articles powered by AMS MathViewer
- by Bo-Yong Chen, Yuanpu Xiong and Liyou Zhang;
- Proc. Amer. Math. Soc. 152 (2024), 2953-2961
- DOI: https://doi.org/10.1090/proc/16799
- Published electronically: May 7, 2024
- HTML | PDF | Request permission
Abstract:
We present an equality between the Bergman metric and Carathéodry metric.References
- Stefan Bergman, The kernel function and conformal mapping, Second, revised edition, Mathematical Surveys, No. V, American Mathematical Society, Providence, RI, 1970. MR 507701
- Jacob Burbea, Inequalities between intrinsic metrics, Proc. Amer. Math. Soc. 67 (1977), no. 1, 50–54. MR 481121, DOI 10.1090/S0002-9939-1977-0481121-1
- Jacob Burbea, The Carathéodory metric and its majorant metrics, Canadian J. Math. 29 (1977), no. 4, 771–780. MR 445015, DOI 10.4153/CJM-1977-080-9
- Bo-Yong Chen and Liyou Zhang, On the $p$-Bergman theory, Adv. Math. 405 (2022), Paper No. 108516, 69. MR 4438059, DOI 10.1016/j.aim.2022.108516
- Kyong T. Hahn, On completeness of the Bergman metric and its subordinate metric, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 12, 4294. MR 417459, DOI 10.1073/pnas.73.12.4294
- Kyong T. Hahn, Inequality between the Bergman metric and Carathéodory differential metric, Proc. Amer. Math. Soc. 68 (1978), no. 2, 193–194. MR 477166, DOI 10.1090/S0002-9939-1978-0477166-9
- K. H. Look, Schwarz lemma in the theory of functions of several complex variables, Acta Math. Sinica 7 (1957), 370–420 (Chinese, with English summary). MR 121503
- K. H. Look, Schwarz lemma and analytic invariants, Sci. Sinica 7 (1958), 453–504. MR 106294
Bibliographic Information
- Bo-Yong Chen
- Affiliation: School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
- Email: boychen@fudan.edu.cn
- Yuanpu Xiong
- Affiliation: School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
- MR Author ID: 1447964
- ORCID: 0000-0003-1132-8004
- Email: ypxiong@fudan.edu.cn
- Liyou Zhang
- Affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100048, People’s Republic of China
- Email: zhangly@cnu.edu.cn
- Received by editor(s): September 7, 2023
- Received by editor(s) in revised form: December 23, 2023
- Published electronically: May 7, 2024
- Additional Notes: The first two authors were supported by National Natural Science Foundation of China, No. 12271101. The third author was supported by National Natural Science Foundation of China, No. 12071310.
- Communicated by: Harold P. Boas
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2953-2961
- MSC (2020): Primary 32F45
- DOI: https://doi.org/10.1090/proc/16799
- MathSciNet review: 4753280
Dedicated: In memory of Professor Qi-Keng Lu