From Kähler Hyperbolicity to Balanced Hyperbolicity

Key Points

• The aim is to explore manifolds with certain positive and hyperbolic properties, particularly focusing on Kähler hyperbolicity.
• Reviewed existing literature on Kähler hyperbolicity.
• Explored applications of hyperbolic classes in various contexts.
• Discussed achievements in generalizing these concepts as birational invariants.
• Established connections between Kähler hyperbolicity and broader classes of hyperbolic objects.
• Highlighted several applications of these properties in geometry and topology.