On solvability of nonlinear partial differential systems of any order in the complex plane
Complex Variables
2011-09-20 v2 Analysis of PDEs
Abstract
We prove a general existence theorem for nonlinear partial differential systems of any order in one complex variable. A special case of first order contains a well-known theorem of Nijenhuis and Woolf concerning local existence of J-holomorphic curves on almost complex manifolds. As an application to differential geometry, we prove that non constant harmonic map always exists locally from a Riemann surface to a Riemannian manifold with a prescribed tangent vector at a given point.
Keywords
Cite
@article{arxiv.1109.3325,
title = {On solvability of nonlinear partial differential systems of any order in the complex plane},
author = {Yifei Pan},
journal= {arXiv preprint arXiv:1109.3325},
year = {2011}
}