Counterexamples to Bloch's Principle and its Converse in Several Complex Variables
Kuldeep Singh Charak, Rahul Kumar
TL;DR
This paper presents counterexamples to Bloch's principle and its converse in several complex variables, along with normality criteria and Picard-type theorems that extend classical results to higher dimensions.
Contribution
It provides the first known counterexamples to Bloch's principle and its converse in multiple complex variables, and establishes new normality criteria and Picard-type theorems in .
Findings
Counterexamples to Bloch's principle in several complex variables
Normality criteria leading to counterexamples of the converse principle
New Picard-type theorems in
Abstract
In this paper, besides a counterexample to Bloch's principle, normality criteria leading to counterexamples to the converse of Bloch's principle in several complex variables are proved. Some Picard-type theorems and their corresponding normality criteria in are also obtained.
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Taxonomy
TopicsMathematical functions and polynomials · Meromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems