A note on the PDE approach to the $L^\infty$ estimates for complex Hessian equations on transverse K\"ahler manifolds

Abstract

We adapt the PDE approach of Guo-Phong-Tong and Guo-Phong-Tong-Wang [17, 18] to prove an $L^\infty$ estimate for transverse complex Monge-Amp\`ere equations on homologically orientable transverse K\"ahler manifolds. As an application, we obtain a purely PDE proof of the regularity of Calabi-Yau cone metrics on Q-Gorenstein T-varieties.