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April, 2001 Blow-up solutions for ordinary differential equations associated to harmonic maps and their applications
Takeyuki NAGASAWA, Atsushi TACHIKAWA
J. Math. Soc. Japan 53(2): 485-500 (April, 2001). DOI: 10.2969/jmsj/05320485

Abstract

In this paper, the blow-up of solutions of ordinary differential equations, which are deduced from the equation of equivariant harmonic maps, is studied. Its direct consequence is the non-existence or existence result of equivariant harmonic maps between warped product manifolds. As another application we prove the non-existence of a harmonic map from an Euclidean space to a Hadamard manifold with a certain nondegeneracy condition at infinity, provided sectional curvatures of the Hadamard manifold are bounded from above by a slowly decaying negative function of the distance from a fixed point.

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Takeyuki NAGASAWA. Atsushi TACHIKAWA. "Blow-up solutions for ordinary differential equations associated to harmonic maps and their applications." J. Math. Soc. Japan 53 (2) 485 - 500, April, 2001. https://doi.org/10.2969/jmsj/05320485

Information

Published: April, 2001
First available in Project Euclid: 9 June 2008

zbMATH: 1008.58015
MathSciNet: MR1815144
Digital Object Identifier: 10.2969/jmsj/05320485

Subjects:
Primary: 58E20
Secondary: 34A34

Keywords: blow-up solutions , equivariant hamonic maps , Harmonic Maps , rotationally nondegeneracy conditions , warped product manifolds

Rights: Copyright © 2001 Mathematical Society of Japan

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Vol.53 • No. 2 • April, 2001
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