Biharmonic map
In the mathematical field of differential geometry, a biharmonic map is a map between Riemannian or pseudo-Riemannian manifolds which satisfies a certain fourth-order partial differential equation. A biharmonic submanifold refers to an embedding or immersion into a Riemannian or pseudo-Riemannian manifold which is a biharmonic map when the domain is equipped with its induced metric. The problem of understanding biharmonic maps was posed by James Eells and Luc Lemaire in 1983. The study of harmonic maps, of which the study of biharmonic maps is an outgrowth (any harmonic map is also a biharmonic map), had been (and remains) an active field of study for the previous twenty years. A simple case of biharmonic maps is given by biharmonic functions.
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Biharmonic map
In the mathematical field of differential geometry, a biharmonic map is a map between Riemannian or pseudo-Riemannian manifolds which satisfies a certain fourth-order partial differential equation. A biharmonic submanifold refers to an embedding or immersion into a Riemannian or pseudo-Riemannian manifold which is a biharmonic map when the domain is equipped with its induced metric. The problem of understanding biharmonic maps was posed by James Eells and Luc Lemaire in 1983. The study of harmonic maps, of which the study of biharmonic maps is an outgrowth (any harmonic map is also a biharmonic map), had been (and remains) an active field of study for the previous twenty years. A simple case of biharmonic maps is given by biharmonic functions.
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In the mathematical field of d ...... given by biharmonic functions.
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1a
Caddeo
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Chen
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Eells
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Jiang
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Lemaire
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Montaldo
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Oniciuc
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Sampson
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1loc
Conjecture 3
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Corollary 2.10
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Definition 5
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Example 12
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Proposition 3.1
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Proposition 3.2
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Proposition 7
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Sections 5−7
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Theorem 3
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Theorem 4.5
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1p
1y
2a
Chen
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2loc
Conjecture 25.B.6
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eq.
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reference
Bang-Yen Chen. "A report on su ...... thematics 22 , no. 2, 117–337.
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Bang-Yen Chen. "Some open prob ...... thematics 17 , no. 2, 169–188.
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Bang-Yen Chen. Pseudo-Riemanni ...... ack, N.J., 2011. xxxii+477 pp.
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Bang-Yen Chen. Total mean curv ...... ack, N.J., 2015. xviii+467 pp.
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Guo Ying Jiang. "2-harmonic ma ...... matica 28 , suppl. 1, 209–232.
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James Eells and Luc Lemaire. S ...... ovidence, R.I., 1983. v+85 pp.
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James Eells, Jr. and J.H. Samp ...... l of Mathematics 86 , 109–160.
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R. Caddeo, S. Montaldo, and C. ...... thematics 12 , no. 8, 867–876.
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S. Montaldo and C. Oniciuc. "A ...... ca Argentina 47 , no. 2, 1–22.
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In the mathematical field of d ...... given by biharmonic functions.
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Biharmonic map
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