Coordinate neighborhoods of arcs and the approximation of maps into (almost) complex manifolds

Details Coordinate neighborhoods of arcs and the approximation of maps into (almost) complex manifolds Coordinate neighborhoods of arcs and the approximation of maps into (almost) complex manifolds

2006-05-18

arxiv.org/abs/math/0605496v1

Mathematics

Complex Variables

Based on the author's doctoral dissertation/

Scientific paper

We study the approximation of J-holomorphic maps continuous to the boundary from ma domain in the complex plane into an almost complex manifold by maps J-holomorphic to the boundary, giving partial results in the non-integrable case. For the integrable case, we study arcs in complex manifolds and establish the existence of neighborhoods biholomorphic to open sets in Euclidean space for several classes of arcs. As an application, we obtain $\mathcal{C}^k$ approximation of holomorphic maps continuous to the boundary into complex manifolds by maps holomorphic to the boundary, provided the boundary is nice enough.

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