# A structure theorem for polyharmonic maps between Riemannian manifolds

## TL;DR

This paper proves that under specific smallness and integrability conditions, polyharmonic maps of any order from complete nonparabolic Riemannian manifolds to any Riemannian manifolds are necessarily harmonic.

## Contribution

It establishes a structure theorem showing that polyharmonic maps reduce to harmonic maps under certain conditions, extending previous results to arbitrary order.

## Key findings

- Polyharmonic maps are harmonic under the given conditions.
- The theorem applies to maps from complete nonparabolic manifolds.
- Conditions involve smallness and integrability constraints.

## 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.