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An inequality of meromorphic functions and its application
Zhaojun Wu1, Yuxian Chen2, Zuxing Xuan3
1School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China.
Thescientificworldjournal
|April 18, 2014
Summary
Researchers used Ahlfors theory to create a new inequality for meromorphic functions in angular domains. This work proves the existence of novel Bloch and pseudo-T singular directions for these functions.
Area of Science:
- Complex Analysis
- Meromorphic Functions
- Geometric Function Theory
Background:
- Meromorphic functions are central to complex analysis.
- Understanding their behavior in specific domains is crucial.
- Previous research has explored singular directions, but new types remain of interest.
Purpose of the Study:
- To establish a fundamental inequality for meromorphic functions within angular domains.
- To investigate and prove the existence of new types of singular directions.
- To extend the application of Ahlfors theory to multiple values.
Main Methods:
- Application of Ahlfors' theory of covering surfaces.
- Development of a novel fundamental inequality.
- Analysis of multiple values of meromorphic functions in angular domains.
Main Results:
- A new fundamental inequality for meromorphic functions in angular domains was established.
- The existence of a Bloch direction for a meromorphic function was proven.
- The existence of a pseudo-T direction for a meromorphic function was demonstrated.
Conclusions:
- The study successfully established a new inequality using Ahlfors theory.
- New singular directions (Bloch and pseudo-T) for meromorphic functions were identified.
- This research contributes to the understanding of meromorphic function behavior in angular domains.
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