Extension of Fujimoto's uniqueness theorems

2023/08/02 by Kai Zhou, Zhou, Kai
Mathematics · #Meromorphic and Entire Functions #Holomorphic and Operator Theory #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2308.01106

Abstract

Hirotaka Fujimoto considered two meromorphic maps f and g of ℂ^m into ℙⁿ such that f^*(H_j)=g^*(H_j) ( 1≤ j≤ q ) for q hyperplanes H_j in ℙⁿ in general position and proved f=g under suitable conditions. This paper considers the case where f is into ℙⁿ and g is into ℙ^N and gives extensions of some of Fujimoto's uniqueness theorems. The dimensions N and n are proved to be equal under suitable conditions. New and interesting phenomena also occur.

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