Polyharmonic maps into the Euclidean space

2013/07/18 by Nakauchi, Nobumitsu, Urakawa, Hajime
#Differential Geometry (math.DG) #FOS: Mathematics #primary 58E20 #secondary 53C43

paper · doi:10.48550/arxiv.1307.5089

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.

Related

• Polyharmonic maps of order k with finite L^p k-energy into Euclidean spaces
• Biharmonic maps into a Riemannian manifold of non-positive curvature
• k-harmonic maps into a Riemannian manifold with constant sectional curvature
• Existence of polyharmonic maps in critical dimensions
• On conservation laws for polyharmonic maps