Hessian equations of Krylov type on compact Hermitian manifolds

Abstract

In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix. Under the assumption of the 𝒞-subsolution, we obtain a priori estimates in Γk−1{\Gamma }_{k-1} cone. By using the method of continuity, we prove an existence theorem, which generalizes the relevant results. As an application, we give an alternative way to solve the deformed Hermitian Yang-Mills equation on compact Kähler threefold.

Keywords

• hessian equations
• hermitian manifolds
• subsolution condition
• 35j60
• 35b45
• 53c55