POLYHARMONIC MAPS OF ORDER k WITH FINITE LpK-ENERGY INTO EUCLIDEAN SPACES

We consider polyharmonic maps φ : (M, g) → En of order k from a complete Riemannian manifold into the Euclidean space and let p be a real constant satisfying 2 ≤ p < ∞. (i) If ∫M|Wk-1|pdυg < ∞ and ∫M|∇̄Wk-2|2dυg < ∞, then φ is a polyharmonic map of order k - 1. (ii) If ∫M|Wk-1|pdυg < ∞ a...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2015-05, Vol.143 (5), p.2227-2234
Main Author: MAETA, SHUN
Format: Article
Language:English
Online Access:Get full text
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Summary:We consider polyharmonic maps φ : (M, g) → En of order k from a complete Riemannian manifold into the Euclidean space and let p be a real constant satisfying 2 ≤ p < ∞. (i) If ∫M|Wk-1|pdυg < ∞ and ∫M|∇̄Wk-2|2dυg < ∞, then φ is a polyharmonic map of order k - 1. (ii) If ∫M|Wk-1|pdυg < ∞ and Vol(M, g) = ∞, then φ is a polyharmonic map of order k - 1. Here, Ws = Δ̄ s-1τ(φ) (s = 1,2,···) and W0 = φ. As a corollary, we give an affirmative partial answer to the generalized Chen conjecture.
ISSN:0002-9939
1088-6826