The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary

Abstract

We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in $\bC^n$. Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian manifolds with boundary that equipped locally conformal Kähler metrics, provided a subsolution.

35 pages + appendix; v4 final version to appear in Annali SNS

References in corpus (4)

• Viscosity solutions to complex Hessian equations
• Pluripotential estimates on compact Hermitian manifolds
• Weak solutions of complex Hessian equations on compact Hermitian manifolds
• On estimates for the Fu-Yau generalization of a Strominger system