Complex Hessian equations with prescribed singularity on compact Kähler manifolds

Chinh H. Lu, Van-Dong Nguyen

Let $(X,\omega )$ be a compact Kähler manifold of dimension $n$ and fix $1\le m\le n$. We prove that the total mass of the complex Hessian measure of $\omega$-$m$-subharmonic functions is n…