Regularity of fully non-linear elliptic equations on Hermitian manifolds. II

Abstract

In this paper we investigate the regularity and solvability of solutions to Dirichlet problem for fully non-linear elliptic equations with gradient terms on Hermitian manifolds, which include among others the Monge-Ampère equation for $(n-1)$-plurisubharmonic functions. Some significantly new features of regularity assumptions on the boundary and boundary data are obtained, which reveal how the shape of the boundary influences such regularity assumptions. Such new features follow from quantitative boundary estimates which specifically enable us to apply a blow-up argument to derive the gradient estimate. Interestingly, the subsolutions are constructed when the background space is moreover a product of a closed Hermitian manifold with a compact Riemann surface with boundary.

The assumption on boundary is further weakened. As a result, main theorems are improved. We also rewrite some places and correct typos to improve readability

References in corpus (3)

• Infinite geodesic rays in the space of Kahler potentials
• Moment maps, nonlinear PDE, and stability in mirror symmetry
• Fu-Yau Hessian Equations

Cited by in corpus (5)

• The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
• On the partial uniform ellipticity and complete conformal metrics with prescribed curvature functions on manifolds with boundary
• The Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with mean concave boundary
• The Neumann problem for a type of fully nonlinear complex equations
• Local $C^0$-estimate and existence theorems for some prescribed curvature problems on complete noncompact Riemannian manifolds