Weak solutions of complex Hessian equations on compact Hermitian manifolds

Abstract

prove the existence of weak solutions of complex in-Hessian equations on compact Hermitian manifolds for the non-negative right-hand side belonging to L-p, p > n/m, (n is the dimension of the manifold). For smooth, positive data the equation has recently been solved by Szekelyhidi and Zhang. We also give a stability result for such solutions.