Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds

Abstract

Let $(M,\omega )$ be a compact Hermitian manifold, and let $\Gamma$ be a symmetric convex cone. We develop a quantitative regularization method for $\Gamma$-admissible functions. As an application, we prove Hölder continuity for every pluripotential solution of complex $m$-Hessian equations whose right-hand sides belong to $L^p$, for $p>\frac{n}{m}$. These results extend to a more general class of complex Hessian equations satisfying the structural condition used by Guo--Phong--Tong.

40 pages. We revised some typos in the statement of Theorem 1.1 and Corollary 1.1