The Monge-Ampère equation for strictly $(n-1)$-convex functions with Neumann condition

Abstract

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.

arXiv admin note: substantial text overlap with arXiv:1903.04231

References in corpus (2)

• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• The Neumann problem of Hessian quotient equations