Taiwanese Journal of Mathematics

A SPACE OF MEROMORPHIC MAPPINGS AND AN ELIMINATION OF DEFECTS

Seiki Mori

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Abstract

This is a summary report of my recent articles. Nevanlinna theory asserts that each meromorphic mapping f of Cm into Pn(C) has few defects. However, it seems that meromorphic mappings with defects are very few. In this report, we shall show that for any given transcendental meromorphic mapping of Cm into Pn(C); there is a small deformation of f which has no Nevanlinna deficient hyperplanes in Pn(C); and also in the case m = 1; there is a small deformation of f which has no Nevanlinna deficient hypersurfaces of degree · d for each given positive integer d; or deficient rational moving targets. Furthermore, we shall show that mappings without Nevanlinna defects are dense in a space of transcendental meromorphic mappings.

Article information

Source
Taiwanese J. Math., Volume 5, Number 3 (2001), 519-533.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500574947

Digital Object Identifier
doi:10.11650/twjm/1500574947

Mathematical Reviews number (MathSciNet)
MR1849775

Zentralblatt MATH identifier
0988.32015

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}

Keywords
nevanlinna theory defect meromorphic mapping

Citation

Mori, Seiki. A SPACE OF MEROMORPHIC MAPPINGS AND AN ELIMINATION OF DEFECTS. Taiwanese J. Math. 5 (2001), no. 3, 519--533. doi:10.11650/twjm/1500574947. https://projecteuclid.org/euclid.twjm/1500574947


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