NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

doi:10.1007/s10473-021-0606-2

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (6): 1887-1895.doi: 10.1007/s10473-021-0606-2

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NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

Daochun SUN¹, Yingying HUO², Fujie CHAI³

1. School of Mathematics, South China Normal University, Guangzhou 510631, China;
2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
3. School of Financial Mathematics&Statistics, Guangdong University of Finance, Guangzhou 510521, China

Received:2021-03-11 Revised:2021-07-11 Online:2021-12-25 Published:2021-12-27
Supported by:
The second author was supported by the National Natural Science Foundation of China (11501127), Foundation for Distinguished Young Talents in Higher Education of Guangdong Province (2014KQNCX068). The third author was supported by the Foundation of Guangzhou Civil Aviation College (18X0428).

Abstract

Abstract: In this paper, we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces. Then, we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces. These results generalize the Montel-type normal criterion of holomorphic curves.

Key words: complex projective spaces, holomorphic curves, holomorphic mappings, normal families, restricted hyperplanes

CLC Number:

30D45

Daochun SUN, Yingying HUO, Fujie CHAI. NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES[J].Acta mathematica scientia,Series B, 2021, 41(6): 1887-1895.

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NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

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