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 $\omega$.

30 pages, 3 figures

References in corpus (4)

• Complex Monge-Ampere equations on Hermitian manifolds
• The Dirichlet problem for degenerate complex Monge-Ampere equations
• The deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds
• Mean curvature flows and isotopy problems