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

Atsushi Atsuji

Research output: Contribution to journal › Article

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 languageEnglish
Pages (from-to)119-138
Number of pages20
JournalPotential Analysis
Volume29
Issue number2
DOIs
Publication statusPublished - 2008 Sep

Fingerprint

Nevanlinna Theory
Meromorphic Function
Error term
Submanifolds
Ricci Curvature
Theorem
Form

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn . / Atsuji, Atsushi.

In: Potential Analysis, Vol. 29, No. 2, 09.2008, p. 119-138.

Research output: Contribution to journal › Article

Atsuji, A 2008, 'A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn ', Potential Analysis, vol. 29, no. 2, pp. 119-138. https://doi.org/10.1007/s11118-008-9091-7
Atsuji A. A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn Potential Analysis. 2008 Sep;29(2):119-138. https://doi.org/10.1007/s11118-008-9091-7
Atsuji, Atsushi. / A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn In: Potential Analysis. 2008 ; Vol. 29, No. 2. pp. 119-138.
@article{9984650c30b641a1bf32d43023a1d1b5,
title = "A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn",
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",
year = "2008",
month = "9",
doi = "10.1007/s11118-008-9091-7",
language = "English",
volume = "29",
pages = "119--138",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in Cn

AU - Atsuji, Atsushi

PY - 2008/9

Y1 - 2008/9

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.

KW - Brownian motion on manifolds

KW - Holomorphic map

KW - Meromorphic function

KW - Minimal submanifold

KW - Nevanlinna theory

UR - http://www.scopus.com/inward/record.url?scp=49749136118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49749136118&partnerID=8YFLogxK

U2 - 10.1007/s11118-008-9091-7

DO - 10.1007/s11118-008-9091-7

M3 - Article

AN - SCOPUS:49749136118

VL - 29

SP - 119

EP - 138

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 2

ER -

Access to Document