Extensions of p-Yosida functions to holomorphic mappings of several complex variables

ABSTRACT

Let M be a complete complex Hermitian manifold with metric $E_M.$ A holomorphic mapping $f:{\mathbf{C}}^m\to M$ is called p-Yosida mapping if $\parallel z{\parallel }^{2-p}{E}_M\left(f\right(z),df(z\left)\right(\xi \left)\right)$ is bounded above for $z,\xi \in {\mathbf{C}}^m$ with $\parallel \xi \parallel =1,$ where $df\left(z\right)$ is the mapping from $T_z\left({\mathbf{C}}^m\right)$ to $T_{f\left(z\right)}\left(M\right)$ induced by f. We formulate and prove a criterion of holomorphic mappings belonging to the class of all p-Yosida mappings and its applications to establish two different analogues of Lappan's five-point theorem.

Keywords:

• Holomorphic mapping
• Hermitian metric
• complex manifold
• normal family

AMS Subject Classifications:

• 32H02
• 30D35
• 32C15

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by NNSF of China – National Natural Science Foundation of China (Grant No. 11701006) and also by NSF of Anhui Province -Natural Science Foundation of Anhui Province (1808085QA02), China.