Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (4): 1631-1644.doi: 10.1007/s10473-022-0420-5

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

Jiaxing HUANG1, Tuen Wai NG2   

  1. 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).

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

CLC Number: 

  • 32H30
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