Treffer: Viscosity Solutions to Degenerate Complex Monge-Ampère Equations

Degenerate complex Monge-Ampere equations on compact Kahler manifolds have recently been studied intensively using tools from pluripotential theory. We develop an alternative approach based on the concept of viscosity solutions and systematically compare viscosity concepts with pluripotential theoretic ones. This approach works only for a rather restricted type of degenerate complex Monge-Ampere equations. Nevertheless, we prove that the local potentials of the singular Kahler-Einstein metrics previously constructed by the authors are continuous plurisubharmonic functions. They were previously known to be locally bounded. Another application is a lower-order construction with a C0-estimate of the solution to the Calabi conjecture that does not use Yau's celebrated theorem.