Holomorphic Deformations of Compact K\"ahler Hyperbolic Manifolds

TL;DR

This paper investigates how compact Kähler hyperbolic manifolds deform under small changes, proposing modified notions of hyperbolicity to better understand their stability and deformation properties.

Contribution

It introduces modified versions of Kähler hyperbolicity to analyze the deformation openness of Gromov's classical concept.

Findings

Proposes new criteria for Kähler hyperbolicity

Establishes initial steps towards deformation stability analysis

Provides insights into the structure of hyperbolic manifolds

Abstract

The goal of this paper is to study the deformations of compact K\"ahler hyperbolic manifolds. We propose slightly modified versions of K\"ahler hyperbolicity as a tool to provide a first step towards investigating the deformation openness of Gromov's classical notion of K\"ahler hyperbolicity.