The Dirichlet problem for mixed Hessian equations on Hermitian manifolds

Abstract

In this paper we study the Dirichlet problem for a class of Hessian type equation with its structure as a combination of elementary symmetric functions on Hermitian manifolds. Under some conditions with the initial data on manifolds and admissible subsolutions, we derive a priori estimates for this complex mixed Hessian equation and solvability of the corresponding Dirichlet problem.

32 pages. arXiv admin note: text overlap with arXiv:2107.12035 by other authors