Abstract:We study the existence and uniqueness of viscosity solutions to complex Hessian equations on a closed Hermitian manifold. We show the viscosity solution exists if the Hessian equation satisfies a determinant domination condition. For uniqueness, we reduce it to the strict monotonicity of the solvability constant in terms of the right hand side, which is still not well understood for the moment. This is based on joint work with Yulun Xu.