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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.02679 |
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| _version_ | 1866910099553910784 |
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| author | Fan, Jiaxuan Wang, Mingwei Yang, Xiaokui Yau, Shing-Tung |
| author_facet | Fan, Jiaxuan Wang, Mingwei Yang, Xiaokui Yau, Shing-Tung |
| contents | In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem for Higgs bundles over compact complex manifolds. Let $ (E,θ) $ be a Higgs bundle over a compact Hermitian manifold $(M,ω_g) $. Suppose that there exists a smooth Hermitian metric $ h_0 $ on $E$ such that the Hermitian-Yang-Mills tensor $ Λ_{ω_g}\left(\sqrt{-1} R^{D^{h_0}}\right) $ of the Higgs connection is positive definite. Then for any Hermitian positive definite tensor $ P\in Γ\left(M,E^*\otimes \bar E^*\right) $, there exists a unique smooth Hermitian metric $ h $ on $E$ such that $$Λ_{ω_g} \left(\sqrt{-1} R^{D^h}\right)=P.$$ We also establish quantitative Chern number inequalities for Higgs bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02679 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | RC-positivity, comparison theorems and prescribed Hermitian-Yang-Mills tensors II Fan, Jiaxuan Wang, Mingwei Yang, Xiaokui Yau, Shing-Tung Differential Geometry 53C55 In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem for Higgs bundles over compact complex manifolds. Let $ (E,θ) $ be a Higgs bundle over a compact Hermitian manifold $(M,ω_g) $. Suppose that there exists a smooth Hermitian metric $ h_0 $ on $E$ such that the Hermitian-Yang-Mills tensor $ Λ_{ω_g}\left(\sqrt{-1} R^{D^{h_0}}\right) $ of the Higgs connection is positive definite. Then for any Hermitian positive definite tensor $ P\in Γ\left(M,E^*\otimes \bar E^*\right) $, there exists a unique smooth Hermitian metric $ h $ on $E$ such that $$Λ_{ω_g} \left(\sqrt{-1} R^{D^h}\right)=P.$$ We also establish quantitative Chern number inequalities for Higgs bundles. |
| title | RC-positivity, comparison theorems and prescribed Hermitian-Yang-Mills tensors II |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2604.02679 |