The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
Abstract
We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori $C^2$ estimates which depend on the initial data on manifolds, the admissible subsolutions and the upper bound of the gradients of the solutions. In some special cases, we obtain the gradient estimates, and hence we can solve the corresponding Dirichlet problem with admissible subsolutions. We also study the Hessian quotient equations and $(m1,m1)$Hessian quotient equations on compact Hermitian manifolds without boundary.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.02412
 Bibcode:
 2019arXiv190502412F
 Keywords:

 Mathematics  Differential Geometry;
 53C55;
 35J25;
 35J60;
 32W20;
 58J05;
 58J32
 EPrint:
 45 pages