Polyharmonic maps into the Euclidean space


Abstract


We study polyharmonic (k-harmonic) maps between Riemannian manifolds with finite j-energies (j=1,\cdots,2k-2). We show that if the domain is complete and the target is the Euclidean space, then such a map is harmonic.

DOI Code: 10.1285/i15900932v38n1p89

Keywords: harmonic map; polyharmonic map; Chen's conjecture; generalized Chen's conjecture

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