Long-time behavior of the Hermitian-Yang-Mills flow on non-K\"ahler manifolds

Zeng Chen; Chao Li; Chuanjing Zhang; Xi Zhang

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arXiv · 2601.05614

Long-time behavior of the Hermitian-Yang-Mills flow on non-K\"ahler manifolds

Zeng Chen·Chao Li·Chuanjing Zhang·Xi Zhang

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Abstract

In this paper, we study the long-time behavior of the Hermitian-Yang-Mills flow over compact Hermitian manifolds. We obtain the monotonicity of lower bound and upper bound of the eigenvalues of the mean curvature along the Hermitian-Yang-Mills flow. In the Gauduchon case, we show that the eigenvalues of the mean curvature converge to geometric invariants determined by the Harder-Narasimhan type. Furthermore, we generalize the Atiyah-Bott-Bando-Siu question to the non-K\"ahler case.

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BibTeX RIS

Zeng Chen, Chao Li, Chuanjing Zhang, Xi Zhang. 2026-01-09. Long-time behavior of the Hermitian-Yang-Mills flow on non-K\"ahler manifolds. https://arxiv.org/abs/2601.05614

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