Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds

Abstract

Let $(X,\omega )$ be a compact connected Hermitian manifold of dimension $n$. We consider the Bott-Chern cohomology and let $[\chi ]\in H_{\text{BC}}^{1,1}(X;\mathbb{R})$. 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 $\omega$.

arXiv comment30 pages, 3 figures

References in corpus (16)

• On the evolution of a Hermitian metric by its Chern-Ricci form
• $C^{2,\alpha }$ estimates for nonlinear elliptic equations in complex and almost complex geometry
• Generalized Kahler Geometry and the Pluriclosed Flow
• (1,1) forms with specified Lagrangian phase: A priori estimates and algebraic obstructions
• Rational curves and special metrics on twistor spaces
• Moment maps, nonlinear PDE, and stability in mirror symmetry
• The deformed Hermitian Yang-Mills equation on three-folds
• Deformed Hermitian Yang-Mills connections, extended gauge group and scalar curvature
• The Dirichlet problem for degenerate complex Monge-Ampere equations
• Complex Monge-Ampere equations on Hermitian manifolds
• Strominger connection and pluriclosed metrics
• Collapsing of the line bundle mean curvature flow on Kähler surfaces
• Stability and the deformed Hermitian-Yang-Mills equation
• Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow
• The deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds
• Mean curvature flows and isotopy problems

Cited by in corpus (1)

• A new flow solving the LYZ equation in Kähler geometry