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 if the domain is complete and the target is the Euclidean space, then such a map is harmonic.

11 pages. arXiv admin note: text overlap with arXiv:1201.6457

Cited by in corpus (2)

• Triharmonic isometric immersions into a manifold of non-positively constant curvature
• Polyharmonic maps of order k with finite L^p k-energy into Euclidean spaces