Higgs bundles over non-compact Gauduchon manifolds

Zhang, Chuanjing; Zhang, Pan; Zhang, Xi

doi:10.1090/tran/8323

Cited by 13 publications

(16 citation statements)

References 33 publications

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“…The above identity (2.5) also works for compact manifolds with nonempty boundary case and some noncompact manifolds case, see Proposition 2.6 in [64].…”

Section: Lemma 21 ([39]mentioning

confidence: 93%

Mean curvature negativity and HN-negativity of holomorphic vector bundles

Li¹,

Zhang²,

Zhang³

2021

Preprint

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In this paper, we study holomorphic vector bundles over compact Gauduchon manifolds. Using the continuity method, we prove the existence of L p -approximate critical Hermitian structure. As its application, we show that a holomorphic vector bundle admits a Hermitian metric with negative mean curvature if and only if the maximum of slopes of all of its subsheaves is negative. Furthermore, we study the limiting behavior of the Hermitian-Yang-Mills flow. We prove the minimum of the smallest eigenvalue of the mean curvature is increasing along the Hermitian-Yang-Mills flow, while the maximum of the biggest eigenvalue is decreasing; we show that they converge to certain geometric invariants. Finally, we give some applications.

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“…The above identity (2.5) also works for compact manifolds with nonempty boundary case and some noncompact manifolds case, see Proposition 2.6 in [64].…”

Section: Lemma 21 ([39]mentioning

confidence: 93%

Mean curvature negativity and HN-negativity of holomorphic vector bundles

Li¹,

Zhang²,

Zhang³

2021

Preprint

Self Cite

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“…Research into the DUY theorem gained momentum in the 1980s, driven by numerous eminent mathematicians, as documented in works such as [1][2][3][4][5]. Over the past two decades, this theorem has continuously piqued the interest of numerous researchers, as evidenced by various publications ( [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references within). On 9 September 2021, Mochizuki was awarded the Breakthrough Prize in Mathematics for his remarkable contributions to the field of twistor D-modules.…”

Section: Introductionmentioning

confidence: 99%

Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold

Cai,

Chaubey,

et al. 2024

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“…It was originally proved by Narasimhan-Seshadri ( [34]), Donaldson ([15,16]) and Uhlenbeck-Yau ( [42]) for holomorphic bundles. There are also many interesting and important generalized Donaldson-Uhlenbeck-Yau theorems (see [4,5,6,9,25,31,32,33,37,44,45] and references therein).…”

Section: Introductionmentioning

confidence: 99%

The Limit of the Yang-Mills-Higgs Flow for twisted Higgs pairs

Pan¹,

Shen²,

Zhang³

2023

Preprint

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In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs over Kähler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension 4, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial twisted Higgs bundle.

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Higgs bundles over non-compact Gauduchon manifolds

Abstract: In this paper, we prove a generalized Donaldson-Uhlenbeck-Yau theorem on Higgs bundles over a class of non-compact Gauduchon manifolds.

Cited by 13 publications

References 33 publications

Mean curvature negativity and HN-negativity of holomorphic vector bundles

Mean curvature negativity and HN-negativity of holomorphic vector bundles

Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold

The Limit of the Yang-Mills-Higgs Flow for twisted Higgs pairs

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