• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.999-1017
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• 2024

In this paper, we study the Neumann problem for the complex Hessian quotient equation ${\frac{{\sigma}_k({\tau}{\Delta}uI+{\partial}{\bar{\partial}u)}}{{\sigma}_l({\tau}{\Delta}uI+{\partial}{\bar{\partial}u)}}}={\psi}$ with 0 ≤ 𝑙 < k ≤ n. We prove a priori estimate and global C¹ estimates, in particular, we use the double normal second derivatives on the boundary to establish the global C² estimates and prove the existence and the uniqueness for the Neumann problem of the above complex Hessian quotient equation.