  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 $\omega$.

Differential Geometry;Analysis of PDEs