Hyperbolicity of Fermat-type curves and their complements

In this paper, by using the generalized Borel theorems in ${\mathbb{C}\mathbb{P}}^2$, we show the hyperbolicity of Fermat type curves and their complement in ${\mathbb{C}\mathbb{P}}^2$. This improves Noguchi-Shirosaki’s and Demailly-El Goul’s degree bounds.