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 ℙk. This is a generalization of Cartan’s Second Main Theorem. As a consequence, we establish a uniqueness theorem for holomorphic mappings which intersect O(k3) many totally geodesic hypersurfaces.
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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).
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Huang, J., Ng, T.W. A Uniqueness Theorem for Holomorphic Mappings in the Disk Sharing Totally Geodesic Hypersurfaces. Acta Math Sci 42, 1631–1644 (2022). https://doi.org/10.1007/s10473-022-0420-5
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DOI: https://doi.org/10.1007/s10473-022-0420-5