The total Hessian mass is monotone in singularity type, and Hessian equations H_m(u)=µ have unique solutions in prescribed singularity classes on compact Kähler manifolds.
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Complex Hessian equations with prescribed singularity on compact K\"ahler manifolds
The total Hessian mass is monotone in singularity type, and Hessian equations H_m(u)=µ have unique solutions in prescribed singularity classes on compact Kähler manifolds.