The Dirichlet Problem for the $k$-Hessian Equation on a complex manifold
Differential Geometry
2019-09-04 v1 Analysis of PDEs
Abstract
We solve the Dirichlet problem for -Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a particular gradient scale. The scale allows us to apply a blow-up argument to obtain control on all necessary norms of the solution.
Cite
@article{arxiv.1909.00447,
title = {The Dirichlet Problem for the $k$-Hessian Equation on a complex manifold},
author = {Tristan C. Collins and Sebastien Picard},
journal= {arXiv preprint arXiv:1909.00447},
year = {2019}
}