The Monge-Ampère Equation for Strictly $(n−1)$-Convex Functions with Neumann Condition

Abstract

A C 2 function on 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.