Fully non-linear elliptic equations on complex manifolds

Abstract

In this paper, we study a broad class of fully nonlinear elliptic equations on Hermitian manifolds. On one hand, under the optimal structural assumptions we derive $C^{2,\hat{I}\pm }$-estimate for solutions of the equations on closed Hermitian manifolds. On the other hand, we treat the Dirichlet problem. In both cases, we prove the existence theorems with unbounded condition.

Lemmas 3.1 and 3.3 improved. arXiv admin note: text overlap with arXiv:2203.04898