A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn

Atsushi Atsuji

doi:10.1007/s11118-008-9091-7

A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cⁿ

Atsushi Atsuji

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show a second main theorem of Nevalinna theory for meromorphic functions on complex submanifolds in Cⁿ . This has a similar form to the classical one and has a remainder term including Ricci curvature. We also give a concrete computation of the remainder term in the case of nonsingular algebraic submanifolds.

Original language	English
Pages (from-to)	119-138
Number of pages	20
Journal	Potential Analysis
Volume	29
Issue number	2
DOIs	https://doi.org/10.1007/s11118-008-9091-7
Publication status	Published - 2008 Sep

Keywords

Brownian motion on manifolds
Holomorphic map
Meromorphic function
Minimal submanifold
Nevanlinna theory

ASJC Scopus subject areas

Analysis

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10.1007/s11118-008-9091-7

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abstract = "We show a second main theorem of Nevalinna theory for meromorphic functions on complex submanifolds in Cn . This has a similar form to the classical one and has a remainder term including Ricci curvature. We also give a concrete computation of the remainder term in the case of nonsingular algebraic submanifolds.",

keywords = "Brownian motion on manifolds, Holomorphic map, Meromorphic function, Minimal submanifold, Nevanlinna theory",

author = "Atsushi Atsuji",

note = "Funding Information: Partially supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.",

year = "2008",

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doi = "10.1007/s11118-008-9091-7",

language = "English",

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AU - Atsuji, Atsushi

N1 - Funding Information: Partially supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.

PY - 2008/9

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N2 - We show a second main theorem of Nevalinna theory for meromorphic functions on complex submanifolds in Cn . This has a similar form to the classical one and has a remainder term including Ricci curvature. We also give a concrete computation of the remainder term in the case of nonsingular algebraic submanifolds.

AB - We show a second main theorem of Nevalinna theory for meromorphic functions on complex submanifolds in Cn . This has a similar form to the classical one and has a remainder term including Ricci curvature. We also give a concrete computation of the remainder term in the case of nonsingular algebraic submanifolds.

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KW - Holomorphic map

KW - Meromorphic function

KW - Minimal submanifold

KW - Nevanlinna theory

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