# Analytically stable Higgs bundles on some non-K\"ahler manifolds

## TL;DR

This paper investigates the existence of Hermitian-Einstein metrics on analytically stable Higgs bundles over certain non-Kähler Hermitian manifolds, expanding the understanding of Higgs bundle stability beyond Kähler geometry.

## Contribution

It provides conditions under which Hermitian-Einstein equations can be solved for stable Higgs bundles on non-compact, non-Kähler Hermitian manifolds, a setting less explored in the literature.

## Key findings

- Existence of Hermitian-Einstein metrics on stable Higgs bundles established
- Conditions identified for solving the Hermitian-Einstein equation in non-Kähler settings
- Extension of stability results to non-compact Hermitian manifolds

## Abstract

In this paper, we study Higgs bundles on non-compact Hermitian manifolds. Under some assumptions for the underlying Hermitian manifolds which are not necessarily K\"ahler, we solve the Hermitian-Einstein equation on analytically stable Higgs bundles.