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 $[\chi ] \in H^{1,1}_{\text{BC}}(X; \mathbb{R})$. 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 $\omega$.