A structure theorem for polyharmonic maps between Riemannian manifolds

Abstract

We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to arbitrary Riemannian manifolds must be harmonic if certain smallness and integrability conditions hold.

References in corpus (4)

• Higher order energy functionals
• Polyharmonic hypersurfaces into space forms
• The stress-energy tensor for polyharmonic maps
• A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions

Cited by in corpus (9)

• Polyharmonic hypersurfaces into space forms
• Polyharmonic hypersurfaces into pseudo-Riemannian space forms
• The stress-energy tensor for polyharmonic maps
• On polyharmonic helices in space forms
• Unique continuation properties for polyharmonic maps between Riemannian manifolds
• On the normal stability of triharmonic hypersurfaces in space forms
• On finite energy solutions of 4-harmonic and ES-4-harmonic maps
• Polyharmonic hypersurfaces into complex space forms
• On conservation laws for polyharmonic maps