On a class of Hessian type equations on Riemannian manifolds

Abstract

In this paper, we consider a class of Hessian type equations which include the $(n-1)$ Monge-Ampère equation on Riemannian manifolds. The \emph{a priori} $C^2$ estimates and the existence of solutions are established.

arXiv comment15 pages

References in corpus (7)

• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• Second Order Estimates and Regularity for Fully Nonlinear Elliptic Equations on Riemannian Manifolds
• Gauduchon metrics with prescribed volume form
• Hermitian metrics, (n-1, n-1) forms and Monge-Ampère equations
• On the second boundary value problem for Monge-Ampere type equations and geometric optics
• Aeppli Cohomology Classes Associated with Gauduchon Metrics on Compact Complex Manifolds
• On the Dirichlet problem for general augmented Hessian equations