# On Cartan's second main theorems for holomorphic curves on M-punctured complex planes

## TL;DR

This paper extends key theorems in Nevanlinna-Cartan theory for holomorphic curves on M-punctured complex planes and improves results on the uniqueness problem related to inverse images of hypersurfaces.

## Contribution

It provides new extensions of fundamental theorems in Nevanlinna-Cartan theory and advances the understanding of uniqueness problems for holomorphic curves.

## Key findings

- Extended Nevanlinna-Cartan theorems for M-punctured planes
- Improved results on the uniqueness of holomorphic curves
- Application to inverse image problems of hypersurfaces

## Abstract

In this paper, we give some extension of fundamental theorems in Nevanlinna - Cartan theory for holomorphic curve on M punctured complex planes. As an application, we establish a result for uniqueness problem of holomorphic curve by inverse image of a hypersurface, it is improvement of some results before [8, 14] in this trend.