A $C^2$ function on $\mathbb{R}^n$ is called strictly $(n-1)$-convex if the sum of any $n-1$ eigenvalues of its Hessian is positive. In this paper, we establish a global $C^2$ estimates to the Monge-Ampère equation for strictly $(n-1)$-convex functions with Neumann condition. By the method of continuity, we prove an existence theorem for strictly $(n-1)$-convex solutions of the Neumann problems.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n1.20.04}, url = {http://global-sci.org/intro/article_detail/jms/15208.html} }