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Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds

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arxiv 2012.00487 v1 pith:VH72SXEF submitted 2020-12-01 math.DG math.AP

Chao-Ming Lin This is my paper · ORCID
classification math.DGmath.AP
keywords equationcompactdeformedhermitianhermitian-yang-millslambdaomegaarctan
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abstract

Let $(X, \omega)$ be a compact connected Hermitian manifold of dimension $n$. We consider the Bott-Chern cohomology and let $[\chi ] \in H^{1,1}_{\text{BC}}(X; \mathbb{R})$. We study the deformed Hermitian-Yang-Mills equation, which is the following nonlinear elliptic equation $\sum_{i} \arctan (\lambda_i) = h(x)$, where $\lambda_i$ are the eigenvalues of $\chi$ with respect to $\omega$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds

    math.AP 2025-06 conditional novelty 5.0 of 10

    Existence of solutions for fully nonlinear elliptic equations on compact almost Hermitian manifolds is established under a sub-slope condition, with applications to the Hessian quotient and deformed Hermitian-Yang-Mil...

  2. Computerized Modeling of Electrophysiology and Pathoelectrophysiology of the Atria -- How Much Detail is Needed?

    physics.comp-ph 2025-05 conditional novelty 1.0 of 10

    A review synthesizing evidence on the required level of detail in atrial computer models for ablation planning, recommending personalized 3D or bilayer models with fiber direction and anisotropic conduction.

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