What is the easiest (and what is the most elementary) way of proving
Newlander-Nirenberg theorem for Riemannian surfaces? I was able to reduce
it to existence of non-trivial harmonic functions (locally) on 2-dimensional
Riemannian manifolds, but this seems to be non-trivial, too. I want to have a construction using 1-dimensional complex analysis and not much else.

A similar question was asked <a href="https://mathoverflow.net/questions/17565/newlander-nirenberg-for-surfaces">here</a>.