• 대한수학회보
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• 제56권5호
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• pp.1327-1340
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• 2019

We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• Korean Journal of Mathematics
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• 제11권1호
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• pp.31-34
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• 2003

In this paper, we introduce the notion of F-harmonic maps and we study the stability of F-harmonic map.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.121-130
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• 2022

In this paper, we prove that every semi-conformal harmonic map between Riemannian manifolds is L-harmonic map. We also prove a Liouville type theorem for L-harmonic maps.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권2호
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• pp.107-111
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• 2002

In this article, we prove various properties and some Liouville type theorems for quasi-strongly p-harmonic maps. We also describe conditions that quasi-strongly p-harmonic maps become p-harmonic maps. We prove that if $\phi$ : $M\;\longrightarrow\;N$ is a quasi-strongly p-harmonic map (\rho\; $\geq\;2$) from a complete noncompact Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive sectional curvature such that the $(2\rho－2)$-energy, $E_{2p-2}(\phi)$ is finite, then $\phi$ is constant.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.559-571
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• 2018

In this paper, we give some results on the stability of f-harmonic maps with potential from or into spheres and any Riemannian manifold. We study the constant boundary-value problems of such maps defined on a specific Cartan-Hadamard manifolds, and obtain a Liouville-type theorem. It can also be applied to the static Landau-Lifshitz equations. We also prove a Liouville theorem for f-harmonic maps with finite f-energy or slowly divergent f-energy.

• 대한수학회지
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• 제55권3호
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• pp.553-574
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• 2018

In this paper, we study harmonic maps and biharmonic maps on the principal G-bundle in Kobayashi and Nomizu and also the warped product $P=M{\times}_fF$ for a $C^{\infty}$(M) function f on M studied by Bishop and O'Neill, and Ejiri.

• East Asian mathematical journal
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• 제19권2호
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• pp.165-171
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• 2003

We show that any F-harmonic map from a compact manifold M to N is necessarily constant if N possesses a strictly-convex function, and prove 'Liouville type theorems' for F-harmonic maps. Finally, when the target manifold is the real line, we get a result for F-subharmonic functions.

• 한국수학사학회지
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• 제18권1호
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• pp.85-92
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• 2005

본 연구는 변분법과 조화사상 사이에 잘 알려진 내용을 개관하고, 조화사상의 성질 및 발전 과정을 정리하고, 구면 위의 라플라스 작용소의 기본 성질을 정리하고, 구면 사이의 고유함수 사상을 구성하기 위하여 스펙트럼과 고유함수를 계산하였다.

• 대한수학회보
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• 제41권3호
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• pp.521-540
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• 2004

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.