On solvability of nonlinear partial differential systems of any order in the complex plane

Yifei Pan

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arXiv · 1109.3325

On solvability of nonlinear partial differential systems of any order in the complex plane

Yifei Pan

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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.

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Yifei Pan. 2011-09-19. On solvability of nonlinear partial differential systems of any order in the complex plane. https://arxiv.org/abs/1109.3325

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