Strongly Gauduchon Hyperbolicity and Two Other Types of Hyperbolicity

Abstract

This paper proposes sG-hyperbolicity as a new tool for studying hyperbolicity on complex manifolds. It demonstrates that this notion leads to a wider class of divisorially hyperbolic manifolds compared to balanced hyperbolicity. We also introduce weakly p-K\"ahler hyperbolic structures and pluriclosed star split hyperbolic metrics as possible new avenues for exploration.