Regularity of degenerate k-Hessian equations on closed Hermitian manifolds

Abstract

In this article, we are concerned with the existence of weak C1,1{C}^{1,1} solution of the kk-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation. The key points are to show the weak C1,1{C}^{1,1} estimates. We prove a Cherrier-type inequality to obtain the C0{C}^{0} estimate, and the complex Hessian estimate is proved by using an auxiliary function, which was motivated by Hou et al. and Tosatti and Weinkove. Our result generalizes the Kähler case proved by Dinew et al.

Keywords

• degenerate k-hessian equations
• optimal regularity
• hermitian manifold
• 35j60
• 35j70