$C^{1,1}$ regularity for degenerate complex Monge-Ampère equations and geodesic rays

Jianchun Chu, Valentino Tosatti, Ben Weinkove

We prove a $C^{1,1}$ estimate for solutions of complex Monge-Ampère equations on compact Kähler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This st…