The Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with mean concave boundary

Abstract

This article studies the Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with \textit{mean concave} boundary in the sense that the mean curvature of the boundary is \textit{nonpositive}. The proof is primarily based on a quantitative boundary estimate. Also, we obtain analogous results in complex variables. In Appendix, the subsolutions are also constructed on certain topologically product manifolds.

References in corpus (5)

• The Space of Kähler metrics (II)
• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• Existence of infinitely many minimal hypersurfaces in closed manifolds
• Curvature estimates for a class of Hessian type equations
• Regularity of fully non-linear elliptic equations on Hermitian manifolds. II