PreprintCC0arXiv
The prescribed Hermitian-Yang-Mills flow I
Abstract
In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow: (∂ h)/(∂ t)=−Λωg(√(−1) Rh)+P where P∈Γ(M,E*⊗E̅*) is a prescribed Hermitian tensor associated with a holomorphic vector bundle E over a Kähler (or Hermitian) manifold (M,ωg). We establish the long-time convergence of the flow to a limiting metric h∞ and use it to solve the prescribed Hermitian-Yang-Mills tensor equation Λωg(√(−1) Rh∞)=P, for a general class of prescribed Hermitian tensors P. The crucial uniform C0-estimate of {h(t)} along the flow is obtained via a parabolic comparison principle.
Related
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- Non-Hermitian Yang--Mills Connections with Vanishing Chern Classes
- A three-block higher-rank deformed Hermitian--Yang--Mills correspondence on ℙ1×ℙ1
- Limiting Behavior of a Class of Hermitian Yang--Mills Metrics, II: Exponential Approximation
- SHARP CONVERGENCE RATES OF THE HERMITIAN-YANG-MILLS-HIGGS ITERATION ON RIEMANN SURFACES
BibTeX
@misc{xiong2026prescribed,
title = {{The prescribed Hermitian-Yang-Mills flow I}},
author = {Zhiyao Xiong and Xaokui Yang and Shing-Tung Yau},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.21062},
eprint = {2606.21062},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21062},
note = {CC0},
}
RIS
TY - UNPB
TI - The prescribed Hermitian-Yang-Mills flow I
AU - Zhiyao Xiong
AU - Xaokui Yang
AU - Shing-Tung Yau
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2606.21062
UR - https://arxiv.org/abs/2606.21062
AB - In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow: (∂ h)/(∂ t)=−Λ_ω_g(√(−1) R^h)+P where P∈Γ(M,E^*⊗E̅^*) is a prescribed Hermitian tensor associated with a holomorphic vector bundle E over a Kähler (or Hermitian) manifold (M,ω_g). We establish the long-time convergence of the flow to a limiting metric h_∞ and use it to solve the prescribed Hermitian-Yang-Mills tensor equation Λ_ω_g(√(−1) R^h_∞)=P, for a general class of prescribed Hermitian tensors P. The crucial uniform C^0-estimate of {h(t)} along the flow is obtained via a parabolic comparison principle.
ER -