Uniform $L^{\infty }$ estimates: subsolutions to fully nonlinear partial differential equations

Abstract

Uniform bounds are obtained using the auxiliary Monge-Ampère equation method for solutions of very general classes of fully non-linear partial differential equations, assuming the existence of a $C$-subsolution in the sense of G. Székelyhidi and B. Guan. The main advantage over previous estimates is in the Kähler case, where the new estimates remain uniform as the background metric is allowed to degenerate.