On Poletsky theory of discs in compact manifolds

TL;DR

This paper introduces a new method for constructing Poletsky discs in compact manifolds using local arc approximation and a Runge-type theorem, advancing the understanding of complex analysis in geometric contexts.

Contribution

It presents a direct construction approach for Poletsky discs, combining local arc approximation with a Runge-type theorem, which is a novel technique in the field.

Findings

Successful construction of Poletsky discs in compact manifolds.

Application of a Runge-type theorem to complex geometric problems.

Enhanced methods for approximating holomorphic discs in complex manifolds.

Abstract

We provide a direct construction of Poletsky discs via local arc approximation and a Runge-type theorem by A. Gournay.