A Runge approximation theorem for pseudo-holomorphic maps

TL;DR

This paper extends the classical Runge approximation theorem to pseudo-holomorphic maps from compact Riemann surfaces to almost-complex manifolds, broadening the scope of approximation results in complex and almost-complex geometry.

Contribution

It proves a Runge approximation theorem for pseudo-holomorphic maps, generalizing classical results to a broader geometric setting.

Findings

Establishes approximation of pseudo-holomorphic maps under certain conditions

Includes applications to some complex varieties

Bridges complex analysis and almost-complex geometry

Abstract

The Runge approximation theorem for holomorphic maps (U -> C) is a fundamental result in complex analysis. The aim of this article is to prove such a result for (pseudo-)holomorphic maps from a compact Riemann surface to a compact (almost-)complex manifold M under certain assumptions. Though the setting is definitively that of pseudo-holomorphic maps it also covers some complex varieties.