A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES

doi:10.1007/s10473-022-0420-5

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1631-1644.doi: 10.1007/s10473-022-0420-5

A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES

黄家兴¹, 吴端伟²

1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China;
2. Department of Mathematics, The University of Hong Kong, Hong Kong, Pokfulam, Hong Kong

收稿日期:2021-04-15 出版日期:2022-08-25 发布日期:2022-08-23
通讯作者: Jiaxing HUANG,E-mail:hjxmath@szu.edu.cn E-mail:hjxmath@szu.edu.cn
基金资助:
Jiaxing Huang was partially supported by a graduate studentship of HKU, the RGC grant (1731115) and the National Natural Science Foundation of China (11701382). Tuen Wai Ng was partially supported by the RGC grant (1731115 and 17307420).

A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES

Jiaxing HUANG¹, Tuen Wai NG²

1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China;
2. Department of Mathematics, The University of Hong Kong, Hong Kong, Pokfulam, Hong Kong

Received:2021-04-15 Online:2022-08-25 Published:2022-08-23
Contact: Jiaxing HUANG,E-mail:hjxmath@szu.edu.cn E-mail:hjxmath@szu.edu.cn
Supported by:
Jiaxing Huang was partially supported by a graduate studentship of HKU, the RGC grant (1731115) and the National Natural Science Foundation of China (11701382). Tuen Wai Ng was partially supported by the RGC grant (1731115 and 17307420).

摘要/Abstract

摘要： In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space $\mathbb{P}^k$. This is a generalization of Cartan's Second Main Theorem. As a consequence, we establish a uniqueness theorem for holomorphic mappings which intersect $O(k^3)$ many totally geodesic hypersurfaces.

关键词: Second Main Theorem, meromorphic connection, totally geodesic hypersurfaces, uniqueness theorem

Abstract: In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space $\mathbb{P}^k$. This is a generalization of Cartan's Second Main Theorem. As a consequence, we establish a uniqueness theorem for holomorphic mappings which intersect $O(k^3)$ many totally geodesic hypersurfaces.

Key words: Second Main Theorem, meromorphic connection, totally geodesic hypersurfaces, uniqueness theorem

中图分类号:

32H30

黄家兴, 吴端伟. A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES[J]. 数学物理学报(英文版), 2022, 42(4): 1631-1644.

Jiaxing HUANG, Tuen Wai NG. A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES[J]. Acta mathematica scientia,Series B, 2022, 42(4): 1631-1644.

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A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES

A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES

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