The DPW method is a construction of harmonic maps from a Riemann surface into a symmetric space using loop groups and an Iwasawa decomposition. Its name abbreviates the surnames Dorfmeister, Pedit, and Wu. The method was developed as a Weierstrass-type representation for harmonic maps (Dorfmeister et al. 1998).
Starting with a holomorphic or meromorphic loop algebra-valued differential
1-form 
,
one first solves
 |
On a region where the relevant Iwasawa decomposition exists, one applies the factorization
 |
where 
belongs to the real loop
group and 
extends holomorphically to the interior
of the parameter disk. The harmonic
map is obtained by projecting 
to the target symmetric space.
Conversely, local harmonic maps satisfying the standard
nondegeneracy hypotheses arise from such potentials.
The DPW method is widely used for surfaces of constant mean curvature because their Gauss maps are harmonic maps. In this setting it generalizes the Enneper-Weierstrass parameterization of minimal surfaces.
